We have four digit cards: 7, 5, 2, and 1. We need to choose two cards each time to make two-digit numbers that satisfy the following conditions: a multiple of 9, a square number, and a factor of 96. The first condition (an even number) has been solved and is 52.

1. Problem Description

We have four digit cards: 7, 5, 2, and

1. We need to choose two cards each time to make two-digit numbers that satisfy the following conditions: a multiple of 9, a square number, and a factor of

9

6. The first condition (an even number) has been solved and is

5

2.

2. Solution Steps

* Multiple of 9: We can form the following two-digit numbers: 75, 72, 71, 57, 52, 51, 27, 25, 21, 17, 15,

1

2. Among these, we need to find a number that is a multiple of

9. * 72 = 9 *

8. Therefore, 72 is a multiple of

9.

* Square number: We need to find a square number among the possible two-digit numbers listed above.

* The square numbers between 10 and 99 are: 16, 25, 36, 49, 64,

8

1. * Among our possible numbers, 25 is a square number ($5^2 = 25$).

* Factor of 96: We need to find a number among the listed two-digit numbers that divides 96 evenly.

* The factors of 96 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48,

9

6. * Among our possible numbers, 12 is a factor of 96 (96 / 12 = 8).

3. Final Answer

* A multiple of 9: 72

* A square number: 25

* A factor of 96: 12