Alex wrote ten different digits on one red card and nine blue cards, only one digit per card. If he multiplies the digit on the red card by the sum of all the digits on the blue cards, he gets 296.

What digit is written on the red card?

The digit written on the red card is 8

Step-by-step explanation:

Allen wrote ten different digits on one red card and nine blue cards. one digit per card is permitted.

He multiplies the digit on the red card by the sum of all the digits on the blue cards he will get 296. Mathematically this can be represented below.

let

digit on the red card = a

sum of digit on the nine blue cards = b

ab = 296

Each card has only a digit in it. Since the cards occupies only ten different digit numbers, the numbers will be 0, 1,2, 3, 4, 5, 6, 7, 8 and 9. Out of the digits only one of them is written on the red card. The remaining number should then be summed.

ab = 296

b = 296/a

If you divide 296 by the only digit on the red card you will get the sum of the digit on all the blue cards. The digit on the red card must be the number from 0 to 9.

Therefore,

let us divide 296 by any single digit from 0 to 9 and know if the value is the sum of the remaining digits.

b = 296/8

b = 37

296 divided by 8 will give 37. Let us check if the remaining digits will sum to 37.

0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 9 = 37

The digit written on the red card is 8