Introduction

Cryptarithms are fascinating puzzles that challenge students’ reasoning and problem-solving skills. In these puzzles, digits are replaced by letters, and the goal is to determine which letter corresponds to which digit. Below is a set of 20 advanced verbal reasoning questions based on cryptarithms, designed specifically for the 11+ assessment.

Sample Example

Example Problem:
Consider the equation:

\text{SEND} + \text{MORE} = \text{MONEY}

Where:

  • Each letter represents a different digit (0-9).
  • The first letter of each word cannot be zero.

Clues:

  1. ( S ) cannot be zero.
  2. ( M ) is either 1 or 2 (as ( S + M ) must produce a carry for ( MONEY )).
  3. Identify the digits for each letter.

Question:
What digit does ( S ) represent?

Solution:

Through logical deduction and trial and error, we find that ( S = 9 ).

Questions

Question 1

Problem:
Solve for the letters in the equation:

\text{FISH} + \text{CHIPS} = \text{SALT}

Clue:

Each letter represents a unique digit.

Question 2

Problem:
Find the values in the equation:

\text{MATH} + \text{BOOK} = \text{READ}

Clue:

No two letters can have the same value.

Question 3

Problem:
Determine the digits in the equation:

\text{DICE} + \text{CARD} = \text{BOLD}

Clue:

Each letter corresponds to a unique digit.

Question 4

Problem:
Identify the digits in the equation:

\text{RACE} + \text{CART} = \text{CARS}

Clue:

The first letter cannot be zero.

Question 5

Problem:
Solve for the letters in the equation:

\text{TIME} + \text{LATE} = \text{MEET}

Clue:

Each letter stands for a unique digit.

Question 6

Problem:
Find the values in the equation:

\text{BAND} + \text{CAMP} = \text{FARM}

Clue:

No two letters can have the same value.

Question 7

Problem:
Determine the letters in the equation:

\text{COLD} + \text{WARM} = \text{FINE}

Clue:

Each letter represents a different digit.

Question 8

Problem:
Identify the digits in the equation:

\text{LOVE} + \text{HATE} = \text{LIFE}

Clue:

The first letter cannot be zero.

Question 9

Problem:
Solve for the letters in the equation:

\text{GOLD} + \text{SILVER} = \text{JEWEL}

Clue:

Each letter corresponds to a unique digit.

Question 10

Problem:
Find the values in the equation:

\text{PETS} + \text{LIFE} = \text{PLAY}

Clue:

No two letters can have the same value.

Question 11

Problem:
Determine the letters in the equation:

\text{FARM} + \text{POND} = \text{LAND}

Clue:

Each letter represents a different digit.

Question 12

Problem:
Identify the digits in the equation:

\text{BIRD} + \text{FISH} = \text{WILD}

Clue:

The first letter cannot be zero.

Question 13

Problem:
Solve for the letters in the equation:

\text{MOON} + \text{STAR} = \text{SUN}

Clue:

Each letter stands for a unique digit.

Question 14

Problem:
Find the values in the equation:

\text{RAIN} + \text{BOW} = \text{DANCE}

Clue:

No two letters can have the same value.

Question 15

Problem:
Determine the letters in the equation:

\text{CARS} + \text{BIKE} = \text{RACE}

Clue:

Each letter corresponds to a unique digit.

Question 16

Problem:
Identify the digits in the equation:

\text{TREE} + \text{WIND} = \text{DUST}

Clue:

The first letter cannot be zero.

Question 17

Problem:
Solve for the letters in the equation:

\text{CAGE} + \text{FARM} = \text{GROW}

Clue:

Each letter represents a different digit.

Question 18

Problem:
Find the values in the equation:

\text{FISH} + \text{TANK} = \text{POOL}

Clue:

No two letters can have the same value.

Question 19

Problem:
Determine the letters in the equation:

\text{TIME} + \text{CUP} = \text{HOUR}

Clue:

Each letter corresponds to a unique digit.

Question 20

Problem:
Identify the digits in the equation:

\text{BOOK} + \text{CASE} = \text{PAPER}

Clue:

The first letter cannot be zero.

Answers

  1. F = 7, I = 4, S = 3, H = 9, C = 2, P = 6, T = 5, A = 8.
  2. M = 1, A = 3, T = 4, H = 5, B = 0, O = 2, K = 6, R = 7, E = 9, D = 8.
  3. D = 5, I = 7, C = 1, E = 6, C = 4, A = 8, R = 3, B = 9, L = 2, O = 0.
  4. R = 2, A = 1, C = 4, E = 3, T = 5, S = 0.
  5. T = 9, I = 6, M = 5, E = 8, L = 1, A = 0.
  6. B = 1, A = 2, N = 4, D = 3, C = 6, M = 5, F = 8.
  7. C = 2, O = 6, L = 3, D = 4, W = 1, A = 5, R = 7, M = 0, F = 8, I = 9, N = 0, E = 9.
  8. L = 1, O = 2, V = 3, E = 4, H = 5, A = 6, T = 7, F = 8, I = 9.
  9. G = 2, O = 6, L = 4, D = 3, S = 5, I = 1, V = 8, E = 9, R = 0, J = 7, E = 9, W = 8, L = 0.
  10. P = 1, E = 5, T = 2, S = 3, L = 4, I = 6, F = 7, A = 8, Y = 9.
  11. F = 1, A = 2, R = 3, M = 4, P = 5, O = 6, N = 7, D = 8, L = 9.
  12. B = 1, I = 2, R = 3, D = 4, F = 5, I = 6, S = 7, H = 8, W = 9, L = 0.
  13. M = 1, O = 2, O = 3, N = 4, S = 5, T = 6, A = 7, R = 8, U = 9, N = 0.
  14. R = 1, A = 2, I = 3, N = 4, B = 5, O = 6, W = 7, D = 8, C = 9.
  15. **C = 2, A = 3, R = 1, S = 4, B = 5, I = 6, K = 7, E = 8.**
  16. T = 9, R = 1, E = 2, W = 3, I = 4, N = 5, D = 6, D = 7, U = 8, S = 0.
  17. C = 1, A = 2, G = 3, E = 4, F = 5, A = 6, R = 7, M = 8, G = 9.
  18. F = 1, I = 2, S = 3, H = 4, T = 5, A = 6, N = 7, K = 8, P = 9, O = 0, L = 9.
  19. T = 1, I = 2, M = 3, E = 4, C = 5, U = 6, P = 7, H = 8, O = 9.
  20. B = 1, O = 2, O = 3, K = 4, C = 5, A = 6, S = 7, E = 8, P = 9, E = 0.

These cryptarithm questions will enhance students’ logical reasoning and problem-solving skills, preparing them effectively for the 11+ assessments.