ExamShortcut
🔍Log in

Coding - Decoding

🔒 Log in to track
high importance~4 Q in Tier 16 formulas⚡ 10 shortcuts7 subtopics
OverviewLearn (7)Formulas (6)Examples (4)Practice (93)
All subtopics·Subtopic 4 of 7

Number coding

🔒 Log in to track
⏱ 5 min read🧩 6 question types🎯 15 practice Q
The idea in one minute

A word is coded as a number built from its letter positions (A = 1 … Z = 26). Most often the number is the sum of the positions. Test the plain sum first; if it does not match, look for one extra step.

01

What number coding is

A word is coded as a number. The number is built from the letter positions. SUN = 19 + 21 + 14 = 54.

Positions run A = 1, B = 2, … Z = 26. The EJOTY anchors make them fast: E = 5, J = 10, O = 15, T = 20, Y = 25.

02

Start with the plain sum

Add the positions of the sample word. Compare the total with the code.

SUN is coded 54. S = 19, U = 21, N = 14, and the sum is 54. That equals the code, so the rule is the plain sum. Then DOG = 4 + 15 + 7 = 26.

Add with anchors, not by counting. S is T − 1 = 19. U is T + 1 = 21. N = 14. The total comes out in seconds.

Rule: Your rule must give the sample's code exactly. If it is off by even 1, it is the wrong rule.

03

A full question, start to finish

"In a certain code, FISH is written as 42. How is TEA written in that code?"

  1. Add the sample's positions: F(6) + I(9) + S(19) + H(8) = 42.
  2. The sum equals the code, so the rule is the plain position sum.
  3. Add the new word: T(20) + E(5) + A(1) = 26.
  4. Write the answer: 26.

One check like this settles the rule. Then every other word in the question uses the same sum.

04

When the sum does not match

Compare the sum with the code and use this table.

What you seeRule
Code = sumplain sum
Code = sum + a fixed numbersum + r
Code = 2 or 3 times the sumsum × k
Short word, big codereverse positions (A = 26 … Z = 1)
A long string of digitspositions written side by side
Letters followed by a numbermixed code

Watch: One sample can fit two rules. BAT = 46 fits "sum × 2" and also "sum + 23". A second sample decides.

05

Reverse positions

Here A = 26, B = 25, … Z = 1. Each letter counts as 27 minus its normal position. CAT = 24 + 26 + 7 = 57.

06

Positions written side by side

Sometimes the positions are not added. They are written one after another. BAD = 2, 1, 4 → 214. CAT = 3, 1, 20 → 3120. FACE = 6, 1, 3, 5 → 6135.

Letters from J onwards take two digits. So when decoding, split the digits carefully. 3120 is C, A, T and not C, A, B, T.

07

Weighted sum

Each position is multiplied by the letter's place in the word, then everything is added.

DAB = 4×1 + 1×2 + 2×3 = 12. So CAD = 3×1 + 1×2 + 4×3 = 17.

Suspect it when no plain sum, sum + r or sum × k fits.

08

Mixed codes

TREE is written as USFF48. The letters moved +1 (TREE → USFF). The number is the position sum: 20 + 18 + 5 + 5 = 48.

Tip: Solve the letter part and the number part separately. Then join them in the sample's order.

For a new word, work out the number part again. Never copy the sample's number.

09

Question types you will see

Each type: how to recognise it, the method step by step, and one question to try.

Type 1very common2 practice Q

Plain position sum

How to spot it:

A word is coded as a number, often between 20 and 80. The question may say 'sum of positions'.

code=∑pi\text{code} = \sum p_i
Method

  1. Add the positions of the sample word's letters.

  2. If the sum equals the code, the rule is the plain sum.

  3. Add the positions of the new word.

Why it works:

The plain sum is the most common number code in these exams.

Try this

In a certain code language, HAT is written as 29. How will PEN be written in that language?

Show solution

  1. H + A + T = 8 + 1 + 20 = 29. The rule is the plain sum.

  2. P + E + N = 16 + 5 + 14.

Answer

35

Type 2common2 practice Q

Reverse-position sum (A = 26 … Z = 1)

How to spot it:

The question says A = 26, B = 25 … Z = 1, or a short word has a large code.

code=∑(27−pi)\text{code} = \sum (27 - p_i)
Method

  1. Change each letter to 27 − its position.

  2. Add them for the sample and confirm the code.

  3. Repeat for the new word.

Why it works:

Reverse positions are the same table read from Z to A.

Try this

In a certain code, EAT is written as 55. How will TEN be written in that code?

Show solution

  1. Reverse values: E = 22, A = 26, T = 7. The sum is 55, so the rule fits.

  2. TEN: T = 7, E = 22, N = 13.

Answer

42

Type 3common2 practice Q

Position sum with an extra step (× k or + r)

How to spot it:

The plain sum of the sample is close to the code but not equal to it.

code=k∑pi+r\text{code} = k\sum p_i + r
Method

  1. Work out the plain sum of each sample.

  2. Find the step: code − sum, or code ÷ sum.

  3. Keep the step that fits every sample.

  4. Apply it to the new word's sum.

Why it works:

One extra operation turns the plain sum into the code.

Try this

In a certain code language, BAT is written as 46 and DOG is written as 52. How will CUP be written in that language?

Show solution

  1. BAT: 2 + 1 + 20 = 23, and 23 × 2 = 46.

  2. DOG: 4 + 15 + 7 = 26, and 26 × 2 = 52. So the rule is sum × 2.

  3. CUP: 3 + 21 + 16 = 40, and 40 × 2 = 80.

Answer

80

Type 4occasional2 practice Q

Weighted sum (position × place in the word)

How to spot it:

No plain sum, sum + r or sum × k explains the code.

code=∑i⋅pi\text{code} = \sum i \cdot p_i
Method

  1. Multiply each letter's position by its place: 1st × 1, 2nd × 2, and so on.

  2. Add the products and check the sample's code.

  3. Do the same for the new word.

Why it works:

Weighting explains codes that no flat sum can reach.

Try this

In a certain code language, DAB is written as 12. How will CAD be written in that language?

Show solution

  1. DAB: 4×1 + 1×2 + 2×3 = 4 + 2 + 6 = 12. The rule fits.

  2. CAD: 3×1 + 1×2 + 4×3 = 3 + 2 + 12.

Answer

17

Type 5occasional2 practice Q

Letters plus a number (mixed code)

How to spot it:

The code is a string like USFF48: letters followed by a number.

Method

  1. Solve the letter part first. It is usually a shift.

  2. Work out the number part for the new word from scratch.

  3. Join both parts in the sample's order.

Why it works:

The two parts are separate small codes, and the number changes with the word.

Try this

In a certain code language, TREE is written as USFF48. How will LEAF be written in that language?

Show solution

  1. Letters: TREE +1 = USFF. Number: 20 + 18 + 5 + 5 = 48.

  2. LEAF +1 = MFBG.

  3. LEAF sum = 12 + 5 + 1 + 6 = 24.

Answer

MFBG24

Type 6common

Positions written side by side

How to spot it:

The code is a long number with no obvious sum. Its digits match the letter positions in order.

Method

  1. Write the position of each letter of the sample.

  2. Check that joining them gives the code.

  3. Write the new word's positions side by side.

Why it works:

Nothing is added, so the code is just the positions in a row.

Try this

In a certain code language, BAD is written as 214 and FACE is written as 6135. How will HIDE be written in that language?

Show solution

  1. BAD = 2, 1, 4 and FACE = 6, 1, 3, 5. Positions are written side by side.

  2. HIDE = 8, 9, 4, 5.

Answer

8945

10

Formula sheet

Position sum
code=∑pi\text{code} = \sum p_i

p = position of a letter, A = 1 … Z = 26.

Sum with an extra step
code=k⋅∑pi+r\text{code} = k \cdot \sum p_i + r

Find k (multiply) or r (add) from the sample. Check with a second sample if one is given.

Weighted sum
code=∑i⋅pi\text{code} = \sum i \cdot p_i

i = place of the letter in the word (1st, 2nd, 3rd …).

Reverse positions
prev=27−pp^{\text{rev}} = 27 - p

Z counts as 1 and A as 26.

11

Shortcuts that save time

⚡ Plain sum first

Work out the position sum of the sample. If it equals the code, you are done. If not, compare: code − sum, then code ÷ sum. Only then try weighted or side-by-side codes.

Example

If SUN is coded as 54, how is MOON coded?

Show solution

  1. S + U + N = 19 + 21 + 14 = 54. So the rule is the plain sum.

  2. M + O + O + N = 13 + 15 + 15 + 14.

Answer

57

⚡ Anchors make sums quick

Letters near E, J, O, T and Y are small hops from 5, 10, 15, 20 and 25. Group them to add fast.

Example

In position-sum coding, is CAT coded as 24?

Show solution

  1. C = 3, A = 1, T = 20.

  2. 3 + 1 + 20 = 24.

Answer

Yes, 24

12

Mistakes to avoid

Where most students lose marks on this subtopic.

Mistake 01

Copying the sample's number into the code of a new word.

Work out the number part again for the new word.

Mistake 02

Summing normal positions when the question says A = 26.

Use 27 − position for every letter.

Mistake 03

Assuming the plain sum without checking the sample.

The rule must give the sample's code exactly.

Mistake 04

Adding the constant to each letter instead of the total.

In 'sum + r' add r once, to the total.

Mistake 05

Adding instead of multiplying in a weighted sum.

Multiply each position by its place, then add.

13

Quick revision

Read this the night before the exam.

  • Positions A = 1 … Z = 26; EJOTY anchors give fast look-ups.

  • Test order: plain sum → sum + r or × k → reverse positions → side by side → weighted.

  • The rule must reproduce the sample's code exactly.

  • Reverse position = 27 − position (A = 26, Z = 1).

  • Mixed codes: code the letters, then add the new word's own number.

  • One sample can fit two rules; use the second sample to decide.

14

Practice: 15 questions

Sets of 10, mixed across the question types above. Every answer has a step-by-step explanation.

Topic test · 10 questions

Suggested time 7 min · wrong answers go to your mistake notebook automatically.

Continue learning