Coding-Decoding

The vocabulary of codes and the four-step method to find a rule.

A code means changing a word into another form by a fixed rule. Four things appear in this whole game:

In every question the rule is not given — you have to find it. Make a habit of these four steps:

The places of the 26 letters, landmarks at every fifth letter and a quick way to count either way.

Code questions run on the places of letters — A is first, B second … Z is twenty-sixth. The full table is below. Under every letter there are two numbers: the upper one is the place counted from A, the lower one the place counted from Z.

Finding places without memorising the whole table

You do not need to memorise the whole table. Just remember five landmark letters, five places apart: E = 5, J = 10, O = 15, T = 20, Y = 25. Every other letter sits right next to a landmark.

• Place of R? The nearest landmark is T = 20; R is two steps before it, so 20 − 2 = 18.
• Place of M? Two steps before the landmark O = 15: 15 − 2 = 13.
• Place of W? Two steps before the landmark Y = 25: 25 − 2 = 23.

Going round the corner

While changing letters you often have to go past Z or before A. Think of the alphabet as a wheel: after Z comes A again, and one step back from A is Z. If the place goes above 26, subtract 26; if it goes below 1, add 26.

A letter and its “mirror”: the 13 pairs, a way to remember them and the “from the back” counting.

Fold the alphabet exactly in the middle so that A sits over Z, B over Y and so on. The two letters that meet are opposite letters. Their places always add up to 27, so the opposite of a letter = 27 − its place.

One important point: M and N are opposites of each other (13 + 14 = 27). So if M turns into N or N into M in a code, it is usually the opposite-letter code.

Moving every letter the same number of places forward (+) or back (−).

Here every letter moves the same number of places forward or back in the alphabet. +2 means A → C, B → D, C → E. To find the rule, take the first pair, work out the gap (go round from Z to A if needed) and then check that the other pairs show the same gap.

Writing the opposite of every letter and spotting this code quickly.

In this code every letter is replaced by its opposite letter — the pair whose places add up to 27. It is easy to spot: if you see pairs like A↔Z and B↔Y, or the very first pair adds up to 27, that is the rule. This code is its own reverse — apply the same rule to the code and you get the original word back.

Codes with alternating, growing, half-and-half or vowel-versus-consonant shifts.

When the gap is not equal in every pair, do not panic — write down the list of gaps under the word, e.g. +1, −1, +1, −1. Whatever pattern you see is the rule.

Reversing the word, swapping the first and the last letters, and rotating the letters.

Some codes do not change the letters at all — they only change their places. How to spot it: count the letters of the code and of the word. If both have exactly the same letters, it is an arrangement code. Then see which letter went where.

When a code is built from two rules: what happened first, what next — and how to undo them.

Sometimes one code carries two rules — say the word is reversed first and then every letter moves one place forward. To spot it, look at the order first (does the code run backwards?), then at the gaps between letters. Checking the two separately opens the rule.

One more thing: when does order matter? When every letter moves equally (say all +1), “shift then reverse” and “reverse then shift” always give the same result. But when the shift changes with position (like +1, −1, +1 …), the two orders give different codes — so keep the order the example shows. While decoding, always undo the last step first.

Making a list of letter pairs from two examples and writing the code of a third word.

In this type every letter has a fixed partner letter but there is no counting rule. Your job is a search: two examples are given and the code of every letter in the new word is found somewhere in those examples.

1. Write the letter pairs of the first example one under another.
2. Add more pairs from the second example.
3. Treat letters whose code shows in both examples as certain — they check your list.
4. Now change the new word one letter at a time using your list.

Finding how the code number relates to the place values of the letters, and ruling out the other rules.

Here the code of a word is a number. Write the place value of each letter (A = 1 … Z = 26) and see how the example’s number was made from those values. Question-setters usually pick one of these ways:

Reading codes from the table and then applying a condition based on the first and the last letters.

In this type you are given a table with a digit against each letter, together with a few conditions. The method is plain — just keep the order firm:

Remember there are only five vowels: A, E, I, O, U. The other 21 letters are consonants. Here is the first table and its conditions:

• if the first and the last letters are both vowels, both are coded as $
• if the first and the last letters are both consonants, both are coded as #
• if the first letter is a vowel and the last is a consonant, interchange their codes
• if the first letter is a consonant and the last is a vowel, the last letter is coded as @

Now a second table with the same four conditions (the conditions are the same, the digits are new):

Finding the two-digit address of a letter in a 5 × 5 table and finding the letter from its address.

Below is a 5 × 5 table of letters (J is left out, so no question uses a word with J). The code of a letter is its address: the row number first, then the column number. A letter in the third row and second column has the code 32.

Message codes with two and three statements, and finding the rest by elimination.

Here the codes belong not to a single word but to a whole sentence. The codes of a sentence’s words are usually written in a different order, so go by what is common, not by position. The method is simple:

1. Pick two sentences that share exactly one word.
2. In the same two codes find the common digit / letter group — that is the code of that word.
3. Repeat with the other pairs of sentences.
4. Find the leftover words by elimination: strike off the word–code pairs already found.

Questions made by renaming colours, objects and directions.

In this type some things are deliberately given other names — for instance “blue is called red”. Then you are asked “what will the colour of the sky be called?” The mind gets tangled here, but the method is just two small steps:

A straight order for spotting the rule in letter codes and number codes.

The commonest reasons for losing marks in code questions and how to avoid them.

• Forgetting the wheel — not adding / subtracting 26 when you go past Y, Z or before A, B.
• Wrong direction — +k from word to code, but −k from code back to word.
• Trusting only the first letter — check the rule on every letter; a changing shift can look fixed on the first one.
• Mixing the two counts — the place from A and the place from Z are different; they add up to 27.
• Skipping the condition — writing the code straight from the table without looking at the first and the last letters.
• Reversing row and column — in a square table the address is always “row, then column”.
• Writing the real name — stopping at the real answer in a swapped-name question and not writing its new name.

Plain shifts, opposite letters, the alphabet and simple number codes.

Before each question ask yourself: “What type of code is this?” Then find the rule and solve.

Alternating shifts, rotation, direct matching, table codes and three-sentence messages.

A mix of mixed rules, decoding, a table with conditions and a square table.

The table and conditions below are for the table questions in this part:

• if the first and the last letters are both vowels, both are coded as $
• if the first and the last letters are both consonants, both are coded as #
• if the first letter is a vowel and the last is a consonant, interchange their codes
• if the first letter is a consonant and the last is a vowel, the last letter is coded as @

Now the questions on the square (row–column) table: