Question

A mystery number is greater than 50 and less than 100. You can make exactly five different rectangles with the mystery number of tiles. (Hint: This means the mystery number is a square number). Its prime factorization consists of only one prime number. What is the mystery number?

Answer 1

Explanation:

The mystery number is 64, sqare number of 8 , the only prime number contributing to it being 2

Being x the mystery number

`50 < x < 100`

The only two sqare numbers that meet this request are 64 and 81.

Not knowing much about the above mentioned rectangles, 81 being the perfect square number of a perfect square number we would consider 64 the only posible answer

Answer 2

81

Explanation:

We know the number is between 50 and 100. The prime factorization consists of only one prime number, so the number must be a perfect square. The possible numbers are 64 and 81.

The rectangles that can be made with 64 tiles are:

1×64, 2×32, 4×16, 8×8, 16×4, 32×2, 64×1

The rectangles that can be made with 81 tiles are:

1×81, 3×27, 9×9, 27×3, 81×1

There are 7 rectangles that can be made with 64 tiles. There are only 5 rectangles that can be made with 81 tiles. Therefore, the mystery number is 81.