Brenda's favourite number

Logic Level 3

Mr and Mrs Tan were once asked to guess which number their only daughter, Brenda, likes. Their four sons, Charles, Darius, Alfred and Eric, however know Brenda's favourite number. The five children each wrote a true statement and a false statement about the mystery number:


  1. The number is divisible by 6.

  2. The number is not greater than 100.


  1. The number is a perfect square.

  2. The units digit of the number exceeds its tens digit by a prime number.


  1. The number is divisible by 3.

  2. There is at least one even digit in the number.


  1. It is a prime number.

  2. The digit sum of the number is 7.


  1. The number is greater than 30.

  2. The number has a composite number of factors.

Assuming the number is a positive integer, can you help Mr and Mrs Tan? What is Brenda's favourite number?


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