Question

Write one digit on each side of 36 to make a four-digit multiple of 36. How many different solutions does this problem have?

Answer 1

Three possible solutions are 1368, 5364, and 9360.

Step-by-step explanation:

• First, we need a number to be a multiple of 36. It means it needs to be a multiple of 4 and a multiple of 9.

Then;

• If the tens digit is 6. Then we can understand that one's digit needs to be 0, 4, or 8. Because we have to make it divisible by four. Thus, we get four numbers as 60, 64, or 68 are divisible by four. These will be last two digits.

• Now, In order to be divisible by 9, the most significant digit needs to be 9 minus the ones digit.
• Therefore, we have solutions only three such solutions as 1368, 5364, and 9360.