Coding-Decoding

In this family the question gives you one word and its code, both of the same length, and asks for the code of a new word (coding) or for the word behind a code (decoding). The only job is to find how each letter travelled. Two very common patterns show themselves in one look: every letter moves the same number of places (a fixed shift), or every letter jumps to its mirror letter (opposite letter). Take the first pair of letters and make two small checks: subtract the positions, and add the positions.

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Look at the figure. ZEBRA becomes CHEUD. Z moves +3 and, because the alphabet is a ring, lands on C. E moves to H, B to E, R to U and A to D. One pair of letters gives the whole pattern; the second pair only confirms it.

To find the shift, take the position of the code letter and subtract the position of the word letter. If the answer is negative, add 26. For Z → C we get 3 − 26 = −23, and −23 + 26 = 3, so the shift is +3. A backward shift is the same idea seen from the other side: −3 is the same as +23, so a code that looks like 'moved back by 3' is also a constant shift.

Same difference every time: fixed shift. Sum 27 every time: opposite letters. Both are checked on the first two letters only.

Questions come in two directions. In coding you apply the shift to a new word. In decoding you are given the coded word and asked for the original, so you apply the shift the other way round: subtract it if the code was made by adding. Both directions use exactly the same pattern; only the arrow is turned around.

A third twist is common in the latest papers: the question asks for the code of the coded word itself, for example 'CRANE is coded as DSBOF; how is DSBOF coded?'. Do not decode anything. Apply the same shift once more to the coded word. With an opposite-letter code the answer is different: applying the mirror twice brings you back to the original word.

Sub-case: opposite letters

In opposite-letter coding each letter is replaced by its mirror letter, the one at the same distance from the other end of the alphabet. A becomes Z, B becomes Y, C becomes X, and M becomes N. You already know the pattern: the position of the opposite letter is 27 minus the position of the letter.

[[fig:1]]

In the figure FISH becomes URHS. F is 6 and U is 21, and 6 + 21 = 27. I is 9 and R is 18, and again 9 + 18 = 27. That sum of 27 is the signature of this type. If every pair of word letter and code letter adds up to 27, the code is plain opposite.

There are three common variants. In the first, only some positions use the opposite and the others keep the same letter, for example odd positions opposite and even positions unchanged. In the second, the opposite is followed by a shift of +1 or +2. In the third, the pair adds up to 25 or 29 instead of 27, which tells you that the opposite has been shifted by 2 (25 means opposite −2, 29 means opposite +2).

In this type the code has the same length as the word, but the difference is not the same for every letter. That does not mean the paper-setter chose steps at random. There is always a pattern, and the same pattern is used again on the new word. So the whole job is: write the step of each position under the word, read the pattern, and repeat it.

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In the figure CLOCK becomes DNRGP and the steps are +1, +2, +3, +4, +5. Three patterns are the classics: growing steps (+1, +2, +3 …), alternating steps (+3, −2, +3, −2 …) and a fixed list that repeats.

There is also a newer form with two lines of steps. Here the odd positions follow one pattern and the even positions follow another, for example odd positions +1, +2, +3 and even positions −1, −2, −3. Treat it as two separate shift lines running through the word.

The latest papers add three more forms.

• Mirror list: the steps read the same from both ends, for example −9, +8, +8, −9 (WARM becomes NIZD). Work out half the list and copy it.
• One odd position: most positions share a step and one differs, for example +11, +1, +1, +1. Here the first letter is replaced by its opposite and the others move +1 (HAND becomes SBOE). The odd position is the one where the sum of word letter and code letter is 27.
• A plain list: a list such as +3, +4, −1, −3, −5 with no visible logic. It does not need one; a new word of the same length takes the same list (see the second figure).

[[fig:1]]

The same idea appears in the pair form: 'CPWG is related to XTTI; NILC is related to IMIE; OKZD is related to ?'. Here the first pair gives the list (−5, +4, −3, +2), the second pair confirms it, and the third group is the question.

One check must come before you call a code variable. Write the word backwards under the code. TEACHER becomes SFIDBFU: the steps along the word look random (−1, +1, +8 …), but TEACHER read backwards is REHCAET, and every letter then moves +1. So that is reverse coding (the next type), not a variable shift.

Write the signed steps under the word, read the pattern, extend it, and check only the positions where the options differ.

In a position-based code no new letter is invented. The code is made of the same letters as the word in a different order, and sometimes a shift is added afterwards. The quickest recognition: sort the letters of the word and of the code. If the two sorted lists match, it is a rearrangement. If they do not match, but the code's first letter is linked to the word's last letter by a clean shift, it is reverse-then-shift.

The forms you will meet, from the most common:

• Whole word reversed (LOTUS → SUTOL).
• First and last letters fixed, the middle reversed (FASHION → FOIHSAN).
• Adjacent pairs swap (positions 1↔2, 3↔4, 5↔6).
• Blocks reverse: the first 2 letters reverse, the next 3 reverse, and so on.
• A fixed permutation (STABLE → SELTBA takes the letters from positions 1 6 5 2 4 3).
• Sorting: alphabetical order (DIRECTOR → CDEIORRT), or vowels first and then consonants.
• Reverse, then a constant shift (BREAD → EBFSC).

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The method for all arrangement forms is the same: number the positions 1, 2, 3 … and write where each code letter came from, for example 2 1 4 3 6 5. Then apply the same list of positions to the new word. If the new word has a different length, a fixed permutation cannot be reused, but the kind of arrangement (reverse, ends fixed, sorted) can.

Reverse, then shift. Compare the code's first letter with the word's last letter. If the difference is a clean shift and the second code letter agrees with the second-last word letter, it is this form. Two things happen to the word, the order changes and the values change, and the options always include the half-done answers.

[[fig:1]]

In the figure BREAD becomes EBFSC. Reading BREAD from the right gives D, A, E, R, B. Now add 1 to each: E, B, F, S, C. The first code letter E comes from the last word letter D, and the last code letter C comes from the first word letter B. The lines in the figure cross because of exactly this.

When the shift is constant, it does not matter whether you reverse first and shift later, or shift first and reverse later; the final string is the same. When the shifts follow a pattern (+1, +2, +3 …), the order matters, so decide from the example where the pattern starts. Do not confuse 'reverse the order of the letters' with 'opposite letters'; the second one is a different type.

Same letters: write the permutation of positions. First code letter linked to the last word letter: reverse, then shift.

In this family different kinds of letters get different treatment. The commonest split is vowels against consonants, but the same idea also covers capital and small letters, odd and even positions, and conditions on the first and last letters. Recent Steno papers print the code in mixed case ("ApPle" is coded as "yrRnC") or ask for numbers (vowels ×2, consonants +4). The questions look new, but the method never changes.

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Mark every letter of the example as V (vowel) or C (consonant), and write its own change beside it. Group the letters by change. A pattern that holds for all the vowels, and another that holds for all the consonants, is the answer. In the figure MOTHER becomes LPSGFQ: the vowels O and E (orange) move +1, the consonants M, T, H, R (blue) move −1.

Mark each letter V or C, find one pattern for each group, and apply them letter by letter.

There are many versions. Consonants may be shifted while vowels stay as they are. Vowels may be replaced by their position numbers. Vowels may shift by 2 and consonants by −3. All of them are solved the same way: sort the letters of the example into two groups, find one pattern per group, and apply the patterns to the new word.

Mixed case. Read the case as part of the instruction: 'vowels become the next letter in lowercase, consonants become the previous letter in UPPERCASE'. Do the shift and the case change as two separate actions on each letter. The options differ in case far more often than in letters, so a wrong case removes an option at once. Y is a consonant unless the question says otherwise.

[[fig:1]]

One letter becomes two. If the code is exactly twice as long as the word, each letter has been replaced by two symbols: its previous and next neighbours, or the letter and its opposite, or the letter and a number. First split the code into groups of two, work out one group, confirm it on a second and keep the group order of the example. Watch the wrap: the previous of A is Z.

Conditional codes. A plain code table is printed, and conditions say when to change it. Look only at the first and the last letters of the word, find the matching condition and apply it to the codes; if no condition matches, the plain code stands. A typical set:
| First and last letters | Change to the plain code |
|---|---|
| both vowels | both coded 9 |
| vowel first, consonant last | interchange the codes of the first and last |
| both consonants | both coded 0 |
| consonant first, vowel last | no condition: plain code |
Interchange means swapping the codes, not the letters.

In a substitution code nothing is calculated. Each letter, symbol, number or name is replaced by a fixed partner, and the same item always gets the same partner. The question gives a few pairs and asks you to read a new item through them. So the whole work is to build a small lookup table and read through it.

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Suppose MASTER is coded as @ # $ % & * and RAIN is coded as * # + ^. Align the first word with its symbols: M is @, A is #, S is $, T is %, E is & and R is *. Align the second word: R is * (this matches the first word, which confirms the table), A is # (again a match), I is + and N is ^. The table in the figure has eight letters. Now any word made of these letters can be coded at once; MINT is @ + ^ %.

Two checks make you safe. First, repeated letters in a given word must have repeated symbols; in MASTER and RAIN the letters R and A repeat across the two words and give the same symbols. Second, if a letter of the new word is not in your table, its symbol cannot be found from the given information, and you must reject every option that pretends to know it.

Build the table by aligning the words, then read the new word letter by letter.

Capital and small letters are different keys. In the latest papers 'A is 11 and a is 1' is a full question: aAa is read as 1, 11, 1, one key per letter, with the case watched at every step. Never merge A and a unless the question says so.

Renaming (meaning-based substitution). Familiar objects are given new names: 'hospital is called school, school is called market …'. The facts of the real world do not change; only the names do. Answer the question in the real world first, then find that real object on the left of the renaming and read what it is called. Stop there: the chain gives each name only once.

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The figure shows the chain table → chair → bed → sofa → desk. Each arrow means 'is called'. Suppose the question is: on what do we sleep? The real answer is a bed (orange). Now look for 'bed' on the left of the chain: bed is called sofa (green). So the answer is sofa. We stop there. We do not carry on to desk, because the chain gives the name for each object only once.

Real answer first, rename once, stop.

The two mistakes are opposite. Some students answer the real object itself (bed), forgetting the renaming. Others keep following the arrows (sofa, then desk) and end too far. If a question asks the other way round, 'what will be called a bed?', then you look for the object on the left of the arrow that points to bed, which is chair.

Here a word is turned into a number. The number is made from the letters in one of a few standard ways, and your job is to find which way the given words follow. There are two families.

Count logics use no positions at all. The code is the number of letters, the number of vowels, the number of consonants, or one of these squared or multiplied by a constant. Rank logics use the alphabet positions: the plain sum of positions, the sum plus or minus a constant, the sum multiplied by a constant, the sum of the digits of the positions, or the same logics applied to the opposite-letter values (27 − p).

[[fig:0]]

In the figure CAT has positions 3, 1 and 20, and their sum is 24. The code is 27, which is the sum plus 3, the number of letters in CAT. Notice the danger: if you test only a three-letter word, '+3' and '+ number of letters' look the same. A word of another length separates them.

Count logics can also be formulas in the number of letters n, and they are easy to miss. For example n − 1 (an 8-letter word is coded 7), n², or n² − 1 (a 4-letter word is coded 15 and a 5-letter word is coded 24). Suspect them when the given words have different lengths and the code grows with the length.

The order of testing saves time. Try the count logics first, because they need no addition. Then the plain sum, then the opposite sum. Compute both given words for each logic and stop at the first logic that explains both.

Test counts first, then the plain sum, then the opposite-letter sum; stop when one logic explains every given word.

There is a shortcut for the opposite-letter sum. Since each opposite value is 27 − p, the sum of the opposite values of an n-letter word is 27n − (plain sum). Work out the plain sum once and you have both.

One convention needs care. In the digit-sum logic, the digits of every position are added once, so a letter at position 19 contributes 1 + 9 = 10. Follow whichever version the given pair confirms, and write this step in your working.

Here every letter becomes its own number, and the numbers are either listed one by one (APPLE → 1, 16, 16, 12, 5) or joined side by side (MONDAY → 1315144125). The number given to a letter can be its plain alphabet position, the position plus or minus a constant, the reverse position (Z = 1, which is 27 − p), or a different treatment for vowels and consonants. The word is often reversed first. There is no sum and no averaging: only the careful handling of one-digit and two-digit positions.

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In the figure TIDE is reversed to EDIT. The positions are E 5, D 4, I 9, T 20. Written side by side they make 5, 4, 9, 20, which is 54920. The first group of the code belongs to the last letter of the word, because the word was reversed.

To encode, reverse the word if the pattern says so, write each position, and join them. Do not put spaces in the answer and do not drop the digits of a two-digit position: 12 stays 12, not 1 or 2.

To decode, you must split the string back into positions. Start from the left and read one digit or two. A group of two digits is possible only when the number is 26 or less and does not start with 0. Many strings can be split in more than one way, so use the length of the options as a guide: if the options have three letters, the code must split into exactly three positions.

Decode by splitting the string into positions between 1 and 26, and use the options to choose between two possible splits.

Finally remember the direction: if the pattern is 'reversed', the first group is the last letter of the word.

A number is changed into another number by a fixed pattern, and you must discover the pattern from the given pairs. The usual patterns are very small: multiply by a constant (×k), multiply and then add or subtract a constant (×k + c), or a digit pattern such as writing the digit sum between the digits.

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In the figure 5 becomes 18 and 8 becomes 30. To find the multiplier, divide the change in the outputs by the change in the inputs: (30 − 18) ÷ (8 − 5) = 12 ÷ 3 = 4. Then find the constant: 18 − 4 × 5 = −2. So the pattern is ×4 − 2, and 12 becomes 4 × 12 − 2 = 46.

One pair can never fix both the multiplier and the constant, so always use two pairs. If the two outputs divide exactly by their inputs and give the same quotient, the pattern is just ×k with no constant.

Multiplier = change in outputs ÷ change in inputs; constant = output − multiplier × input.

Not every pair is ×k + c. The latest papers also give three other shapes.

• Powers: 10 → 1000, 11 → 1331, so each number is cubed and 12 → 1728.
• Digits joined: 8 + 1 = 81, 6 + 3 = 63, so 5 + 4 = 54; the sign only joins the digits.
• Triples: (2, 4, 6) → 12 and (3, 6, 9) → 27 are first × last, so (4, 8, 12) → 48.

Test in this order: is the output a power or a join of the input? Does output ÷ input give a constant? Only then use the two-pair difference method.

A special case is multiplying by 11. For a two-digit number whose digits add up to 9 or less, the answer is the first digit, then the digit sum, then the last digit: 35 × 11 = 385 (3, 3 + 5 = 8, 5). When the digit sum is 10 or more, a carry happens: 78 × 11 = 858 and not 7, 15, 8. So the shortcut is safe only when the digit sum is at most 9.

In an imaginary-language question a few sentences are written in a made-up language. Each word of the sentence has a code word, but the code words are not in the same order as the sentence words. So you cannot read the first code as the first word. The whole question depends on one idea: a word that appears in two sentences has a code that appears in the two coded sentences.

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In the figure, 'red sweet apple' is 'mo lu ka', 'red ripe fruit' is 'ti ne lu' and 'sweet fruit juice' is 'zo ka ti'. Sentences 1 and 2 share the word 'red' and the code 'lu', so red = lu. Sentences 1 and 3 share 'sweet' and 'ka', so sweet = ka. Sentences 2 and 3 share 'fruit' and 'ti', so fruit = ti. The colours in the figure show each pair.

The leftover words are matched with the leftover codes. In sentence 1 the leftover word is 'apple' and the leftover code is 'mo', so apple = mo. In sentence 2 the leftover is ripe = ne, and in sentence 3 it is juice = zo.

For each pair of sentences, underline the common word and the common code; then match what is left over.

Two statements often decide the whole question. If the asked word occurs in exactly two statements, its code is the code that appears in both coded statements, and nothing else needs to be worked out. This is why recent railway papers need only one step ('zip' sits in two statements, so its code is the one code they share), even when every code is a two-letter code.

Sub-case: 'cannot be determined'. Sometimes the statements fix the codes of some words but not the one you are asked. Then no code can be chosen, because the order of the code words never decides which code belongs to which word.

[[fig:1]]

In the figure, 'fast red car' is coded as 'ma ti lo' and 'red bus' is coded as 'ti ke'. The word 'red' is common, and so is the code 'ti', so red = ti. Then in the second statement the leftover word 'bus' takes the leftover code 'ke', so bus = ke. But in the first statement two words, 'fast' and 'car', are left with two codes, 'ma' and 'lo', and nothing tells us which is which. They are orange in the figure. So the code of 'fast' is not determined.

The method is to build the word-code table from the statements, as in an imaginary-language question. Then look at the word asked. If it has exactly one possible code, give that code. If it still has two or more candidates, no option can be correct, and 'cannot be determined' is the answer. Never choose a code from the options just because it is the first one left over.

But do not choose 'cannot be determined' lazily either. If another statement settles the word, the answer is a definite code.

In letter-to-digit coding nothing is calculated. Two or three words are given with their digit codes, and you are asked for the code of a new word, or of a single letter. The whole puzzle is the link between the given words: a letter that appears in two words has the same digit in both.

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Suppose LAMP is 3 8 4 1 and TAME is 2 8 4 6. Put the words one over the other. The letters A and M are common, and their codes 8 and 4 are common. Link them. Now every letter that is left over has a code that is left over too. T is in the first place of TAME, so it takes the first code, 2, and E takes the last code, 6. With the table complete, METAL is 4 6 2 8 3.

The method is always the same: write each word with its code in aligned rows, link every common letter, and write its code once. Fill the remaining codes by position or by elimination. A letter that appears in only one word, in one position, is fixed by that position.

Link the common letters first; what is left over fixes itself by position or elimination.

Two warnings. A digit that belongs to two different letters, or a letter with two different digits, means a wrong link. And if a letter of the target word never appeared in the given words, its code is unknown, and the question cannot be answered unless 'cannot be determined' is an option.

Jumbled digits. First test whether the digits follow the letters. Compare a common letter in the two words: if it has the same digit, the code is ordered and you can link by position. If the same letter seems to carry different digits, the digits are jumbled and position tells you nothing. Then use sets: the digit that sits in only one code belongs to the letter that sits in only that word. In the figure OVAL = 6729 and LEVO = 7946 share the letters O, V, L and the digits 6, 7, 9; the digit 2 is only in OVAL and the letter A is only in OVAL, so A = 2. In the same way E = 4. This works when only one letter is unique to the word asked about; if two letters are unique to it, use the other statements.

[[fig:1]]

A rare twist: digits to letters with a reversed segment. A table such as 1 = B, 2 = R, 3 = A, 4 = I, 5 = N, 6 = S is printed, and a part of the digit string, say the last four digits, is written in reverse. To find the word, undo the twist first and then read the letters: 126543 becomes 123456, which is BRAINS. To code a word, convert the letters to digits first and then twist the stated segment.

In word-property coding every word is coded by itself, through some facts about the word: its first letter, last letter, second letter, number of letters, number of vowels or number of consonants. There is no common word between the given statements, and the words have different lengths. That is how you recognise the type.

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In the figure MOTHER is coded as M 6 2. The first symbol is the first letter (M), the second is the number of letters (6), and the third is the number of vowels (O and E, so 2). The code is read symbol by symbol, and each symbol answers one question about the word.

The method is to list the facts of each given word in a small table, and then match the facts to the code one symbol at a time. Take the first symbol: is it always the first letter, or the last letter, or the second letter? Take the second symbol: is it the length, or the number of vowels, or the number of consonants? A pattern that explains all the given words is the pattern. Then list the same facts for the new word.

For each symbol of the code, find the one property that explains it in every given word.

Be careful with the counts. Total letters, vowels and consonants are three different numbers; keep them separate, and remember that Y is a consonant here. Use only the key printed in the question; never carry a symbol key over from another question.

IDs and roll numbers. The newest papers use the same habit on long codes. A roll number or ID is a string of fixed-length fields, for example the first 3 digits are the region, the next 4 the centre and the last 5 the candidate. Cut the string from the left in the stated lengths, check that the lengths add up to the total (3 + 4 + 5 = 12), and read the field asked. The wrong options are the neighbouring fields or a field cut one digit too early. Another form classifies by a property of the last digit or letter, such as 'a roll number ending in an even digit belongs to Batch 1'.

[[fig:1]]

In matrix coding the letters sit in a grid, and the code of a letter tells you where it sits. The code is the row number first, then the column number, unless the question says otherwise. So the work is only reading the grid carefully.

[[fig:0]]

In the first figure the rows are 0 to 4 and the columns are 0 to 4. The letter P is in row 1, column 0, so P is 10. L is in row 0, column 1, so L is 01. The word PLANT is 10, 01, 02, 13, 14, written together as 1001021314.

Two layouts are seen in exams. In layout A there are two separate matrices with separate digit sets, for example one with row digits 0 to 2 and column digits 0 to 4 and a second with 5 to 7 and 5 to 8. Then every letter has exactly one code, and the digits tell you which matrix to look in. In layout B one matrix has two labels on every row and two labels on every column.

[[fig:1]]

In the second figure the rows are labelled 0 to 4 on the left and 5 to 9 on the right, and the columns are labelled 0 to 4 on top and 5 to 9 at the bottom. The letter H sits in row 0 and column 1, so its row label is 0 or 5 and its column label is 1 or 6. So H can be written as 01, 06, 51 or 56. A letter may have several correct codes, and the options decide.

Write the code of each letter first (all possible codes in layout B), then match whole option strings; one wrong letter removes an option.

The newest form uses one 6 × 6 grid with row numbers on the left and column numbers on top, and the code of a letter is written as (row, column). The same letter can sit in two cells, for example A, E, O and R in the grid below (the bottom two rows repeat letters of the top rows). Such a letter has two correct codes, and the options are built from the wrong cells. A letter that appears only once, like M, K or D, has exactly one code.

[[fig:2]]

Binary coding writes numbers with only two symbols, 0 and 1. Each place has a value, and from the right the place values are 1, 2, 4, 8, 16, 32, 64, doubling each time. A digit 1 means 'this place value is used'; a digit 0 means 'it is not used'. The number is the sum of the place values that carry a 1.

[[fig:0]]

In the figure the place values are written above the digits. The digit 1 appears under 16, 8 and 1, so the number is 16 + 8 + 1 = 25, written in binary as 11001 (the leading zeros are dropped).

To convert a decimal number to binary, subtract the largest place value that fits, write 1 for it, and repeat with what is left; write 0 for every place value you skip. For 25: the largest place value that fits is 16 (25 − 16 = 9); next 8 fits (9 − 8 = 1); 4 and 2 do not fit; 1 fits. So the digits under 16, 8, 4, 2, 1 are 1, 1, 0, 0, 1.

To read a binary number, add the place values under the 1s. For 11011 the place values are 16, 8, 4, 2, 1 and the 1s are under 16, 8, 2 and 1, so the number is 16 + 8 + 2 + 1 = 27.

Some questions use a star-dot form: a dot stands for 0 and a star stands for 1, exactly as the question says. Always use the key printed in the question.

Write the place values 64, 32, 16, 8, 4, 2, 1 above the digits, and add the ones that carry a 1.

Two newer forms appear in the latest papers. In the first, the question names two symbols, such as Δ and β, and says that 0 is Δ and 1 is β; the number asked is written in binary and then every 0 and 1 is replaced by its symbol. In the second, a word is coded as a string of 0s and 1s by a property of its letters: in HABITAT = 0101010 and UNDERNEATH = 1001001100 every vowel is 1 and every consonant is 0. Always find the key from the given examples before you code anything.

The same letter logic appears in letter-group series, in odd one out among letter groups, and in series of single letters. These questions ask for the next term or the different group, not for a code, but the working is the same: positions, differences, and the wrap after Z. (Analogies between letter groups such as 'ABCD is related to EFGH' are in the type on variable shifts; words and numbers in odd-one-out are in the chapters on Classification and Analogy.)

[[fig:0]]

For a series, never read across the term. Line the terms up and read down each column. In the figure the terms are CFI, EHK, GJM. Column 1 is C, E, G, so it moves +2 each time. Column 2 is F, H, J, +2. Column 3 is I, K, M, +2. The next term is therefore I L O. Each column may have its own step, and the steps may be different: +3 in one column, −2 in the next.

For an odd one out, take the differences between neighbouring letters inside each group. Three groups give the same differences and one gives different ones. If that does not separate them, compare the first letters of the groups, then the last letters.

In a series, read each column on its own; in a single-letter series, take the gaps; in an odd one out, compare position by position.

[[fig:1]]

A series of single letters has no columns, so write the positions and take the gaps. In A, C, F, J, O the positions are 1, 3, 6, 10, 15 and the gaps 2, 3, 4, 5 grow by 1, so the next gap is 6 and the next letter is U. Compare the gaps with familiar lists: +1, +2, +3 …; the odd numbers 1, 3, 5, 7; the squares 1, 4, 9, 16; the primes. If the letters look like the initials of months (J F M A M J J A S) or Roman numerals, test that idea first. Past 26, subtract 26.