One of the really pleasurable sensations of having young children is the humiliation associated with homework help. Our second grader's current math homework has an "extra credit"--small consolation!--problem concerning "magic pentagons." The object is to use the numbers 1 through 10, once each, so that the sum of the numbers on the fives sides of the adjoining figure are all the same. Someone is off to a bad start on this one: since the "average" number is 5.5, and 3 x 5.5 = 16.5, it seems reasonable to assume that the best candidates for the one common sum are 16 and 17--in which case there is already no solution for the "northwesterly" and "northeasterly" sides, 10 being the largest available number.

But my initial efforts, conducted while the second grader was sound asleep, didn't yield any good results, either. Having after an embarrassing amount of time come up with a solution, I now see that I was handicapped by the assumption that the corner slots, which have to be used for two sums, must probably be in the middling range. Once I out of frustration dropped that notion, it didn't take much longer to come up with the following solution (proceeding clockwise from the "pinnacle," and as it happens preserving the 1 already filled in): 1, 8, 7, 6, 3, 9, 4, 2, 10, 5. That is, the sums on the five sides are:

1 + 8 + 7 = 16

7 + 6 + 3 = 16

3 + 9 + 4 = 16

4 + 2 + 10 = 16

10 + 5 + 1 = 16.

Next morning, when I showed the second grader my handiwork, she was visibly pleased, and painstakingly copied my work into the space provided on her homework sheet. I asked whether she thought she should add a note indicating that actually her dad had done it. She thought for only a second before answering, "No." I thought that was okay because, honestly, I suspect Ms. Kuhlmann is smart enough to know that every kid getting extra credit this week has at least one nerd for a parent.

Right? If it took me a whole news show plus Jimmy Fallon's monologue to get it, the problem is not really fit for second graders. Right? Hoping.

## Comments