# Where has the last dollar gone?

Lately I have found different versions of this puzzle, I was wondering if it has a name or belongs to a specific kind, so that I can understand it better. Here it is:

Peter got \$10 from his father, \$10 from his mother and went to buy some groceries. He spent only \$17. Once he is back home he gives back \$1 to his father, \$1 to his mother and he keeps \$1 for himself.

In the end his mother spent \$9, his father spent \$9 and that is \$18. Plus the dollar he kept, \$19. Where has that last dollar gone?

• Those crazy Americans... When will they finally use proper SI units for their money instead of these MathJax markers? Commented Feb 7, 2018 at 23:35

This type of puzzle (typically called the missing dollar puzzle in this case) is referred to as an informal fallacy puzzle. The general idea is that the logic that is presented to the user appears at first glance to be correct, but in actuality has an error in it.

In this case, the 9 spent by his father and 9 spent by his mother together equal the 17 spent at the store plus the dollar that he kept. Adding the dollar he kept to that again to get 19 is the error. It is already accounted for.

The truth is Mum and Dad both spent 9.50. $$17 / 2 = 8.5$$ After they were given 1 back. $$8.5 + 1 = 9.5$$ $$9.5 \times 2 = 19$$

19 plus 1 that he kept for himself you have your initial 20.

• Mum and Dad both spent 9 for a total of 18. Of that, Peter spent 17 at the shop and kept 1. Commented Sep 30, 2016 at 9:01
• Your wording is a bit funny, but you are correct that mom and dad spent 9.50 each. 9.00 each on the groceries, and 0.50 each in the form of the kept dollar. Commented Jun 28, 2017 at 16:24
• @ArthurDent That's mixed up. They spent 9.00 each (10 each with 1 back after), 8.50 each went to cover the 17.00, remaining 1.00 went to the son.
– JMac
Commented Jul 9 at 17:51