Six cards numbered 1 through 6 are placed in a hat. One card is taken from the hat. The unit's digit of the sum of the numbers on the remaining cards are 9. What was the number on the card taken from the hat?

Add up the numbers from 1 to 6

Looks like the sum of the remaining numbers is 19
So what number is missing?

To find the number on the card taken from the hat, we need to determine the sum of the numbers on the remaining cards.

Let's start by considering the sum of the numbers 1 through 6, which is 1 + 2 + 3 + 4 + 5 + 6 = 21.

Since the unit's digit of the sum of the remaining cards is 9, the tens digit of the sum should be a whole number greater than or equal to 2.

Let's try subtracting 9 from the sum of the numbers 1 through 6 to see if we get a number with a tens digit greater than or equal to 2:

21 - 9 = 12

The tens digit of 12 is 1, which is less than 2. So the number we subtracted (9) is not the number taken from the hat.

Now, we can try subtracting 19 from the sum of the numbers 1 through 6 to check if the tens digit is greater than or equal to 2:

21 - 19 = 2

The tens digit of 2 is less than 2, so the number we subtracted (19) is also not the number taken from the hat.

Finally, let's subtract 29 from the sum of the numbers 1 through 6:

21 - 29 = -8

The tens digit of -8 is less than 2, so again, the number we subtracted (29) is not the number taken from the hat.

Since subtracting 9, 19, and 29 didn't give us a number with a tens digit greater than or equal to 2, the only possibility left is to subtract 39 from the sum of the numbers 1 through 6:

21 - 39 = -18

The tens digit of -18 is less than 2, so the number we subtracted (39) is also not the number taken from the hat.

Therefore, the only remaining possibility is to subtract 49 from the sum of the numbers 1 through 6:

21 - 49 = -28

The tens digit of -28 is less than 2, so again, the number we subtracted (49) is not the number taken from the hat.

Since all other possibilities have been eliminated, the number taken from the hat must be the only remaining number, which is 5.

Therefore, the number on the card taken from the hat is 5.