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Number Riddles — Mystery Number

Each puzzle gives a set of clues about a hidden two-digit number. Use all of the clues together to work out the one number that fits them all.

Example

What two-digit number fits all of these clues?

  • Clue 1: The sum of its digits is 9.
  • Clue 2: Its factors, apart from the number itself, add up to 21.
  • Clue 3: When it is divided by 5, the remainder is 3.
The number is 18
  1. 1.

    What two-digit number fits all of these clues?

    • Clue 1: Both of its digits are odd.
    • Clue 2: When it is divided by 7, the remainder is 4.
    • Clue 3: When it is divided by 4, the remainder is 3.
    • Clue 4: It is a prime number.
    The number is
  2. 2.

    What two-digit number fits all of these clues?

    • Clue 1: When it is divided by 7, the remainder is 5.
    • Clue 2: It is an odd number.
    • Clue 3: When it is divided by 3, the remainder is 2.
    • Clue 4: When it is divided by 5, the remainder is 4.
    The number is
  3. 3.

    What two-digit number fits all of these clues?

    • Clue 1: When it is divided by 4, the remainder is 3.
    • Clue 2: When it is divided by 5, the remainder is 4.
    • Clue 3: When it is divided by 6, the remainder is 5.
    The number is
  4. 4.

    What two-digit number fits all of these clues?

    • Clue 1: It is a multiple of 4.
    • Clue 2: It is a multiple of 6.
    • Clue 3: When it is divided by 7, the remainder is 6.
    The number is
  5. 5.

    What two-digit number fits all of these clues?

    • Clue 1: It is an even number.
    • Clue 2: It is a multiple of 7.
    • Clue 3: The sum of its digits is 6.
    The number is