Alex wrote nine different positive digits on one red card and eight blue cards, only one digit per card. The product of all the digits on the blue cards is 72576.

What digit is written on the red card?

Answer: 5 is written on the red card.

Step-by-step explanation:

Given that the product of all the digits on the blue cards is 72576.

That is:

4! * 9 * 8 * 7 * 6

= 24 * 3024

= 72576

And the nine different positive digits will be 1 2 3 4 5 6 7 8 9

4! = 4 * 3 * 2 * 1

So, 5 is missing from the product of above number that gave 72576.

Therefore, 5 is the digit is written on the red card