Question

A number between 1 and 150 is written on a piece of paper.

You are given three clues to help you work out the number written on the piece
of paper.
Clue 1: It is one more than a square number.
Clue 2: It is three less than a cube number.
Clue 3: It is not a prime number.
Use each of the clues above to refine your search.
Enter the list of numbers obtained after each clue to finally find the number
written on the piece of paper.

Answer 1

Answer 122

Explanation:

Let's go through the clues one by one and narrow down the possibilities:

• Clue 1: It is one more than a square number.

Possible squares between 1 and 150: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.

Numbers one more than these squares: 2, 5, 10, 17, 26, 37, 50, 65, 82, 101, 122, 145.

• Clue 2: It is three less than a cube number.

Possible cubes between 1 and 150: 1, 8, 27, 64, 125.

Numbers three less than these cubes: -2, 5, 24, 61, 122.

Using these 2 clues: numbers may be: 5, 122

• Clue 3: It is not a prime number.

From the previous list, remove prime numbers: 5.

The number that satisfies all three clues is 122.

So, the number written on the piece of paper is 122.