Write one digit on each side of 10 to make a four digit multiple of 72. How many different solutions does this problem have? The possible solution are ...

If we write 4 to each side of 10, we will get a four digit number 4104, which is a multiple of 72.

To find out other possible solutions, first start with 1 in front of 10.

Now, divide 110 by 72.

The remainder is 38.

We are going to put one more digit after 10.

So, let us check if there is any three digit number whose first two digits are 38 and which is a multiple of 72.

There is no such number since 5 * 72 = 360 and 6 * 72 = 432.

So, there is no four digit number whose first three digits are 110 and which is a multiple of 72.

If we try like this, we can find 4104 is the only solution.