On our walks home from school, my 8-year-old son has been telling me of a math problem that he has not been able to solve. Yesterday, after a week of not finding a solution, he wrote down the problem on paper for us to investigate together. Here is the task in my own words:
Distribute all of the numbers in [5, 15] into boxes A and B. The numbers in box A must sum up to an even number, while the numbers in box B must sum up to an odd number.
My son had been trying to solve this by generating random distributions, but he had not been able to make it work. I suggested that we step back a second to see what must be true of each box. Here’s what we reasoned:
After school today we stopped in and asked my son’s teacher if we were misinterpreting the problem statement somewhere. I tried to walk through the proof that there was no distribution, but I failed to convince her. Probably because I didn’t want to be one of those parents. Or probably because phrases like “an even number of odds” get really disorienting.
The teacher was kind enough to check the solution manual for us. But she found that the provided answer incorrectly had even sums in both boxes. My son and I felt vindicated. She apologized to my son for all the time he spent. We did not accept her apology as the unsolvable problem was more fun than a solvable one.