My family just had the pleasure of a visit from a friend I have known since first grade. Ever since we were kids, my friend and I would try to stump each other with math/logic problems we had heard about (or sometimes, invented ourselves). We went back and forth today, and these two were deemed the most fun — give them a shot if you haven’t heard them before. Answers after the jump.

His best to stump me:

Many numbers are the sum of consecutive digits, for example 29 is equal to 14+15 and 66 is equal to 21 + 22 + 23. Between 100 and 200, there is only one number that is NOT the sum of consecutive digits. What is it?

My best to stump him:

You are in the basement of a house and on the wall are three identical-looking light switches. Two of them are broken and one of them works, but the light that the working switch turns on is in the attic. If you could only make one trip to the attic, how would you determine which of the three switches is the one that works?

Answer to his best stumper:

The easiest way to figure this out is to try it with low numbers and work out which ones aren’t expressable as the sum of consecutive digits. You will see a pattern right away: 2, 4, 8, 16 etc. The only number following that pattern in the specified range is 128 (2 to the power of 7). My friend pointed out that there are many variants of the problem, one could just as easily make the range 200 to 400 (answer = 256), 500 to 1000 (answer = 512) etc.

Answer to my best stumper:

The trick here is to find another data point besides light to tell which switch turns on the bulb, and it’s warmth. Here’s how: Turn on switch number 1 for ten minutes and then turn it off, immediately turning on switch #2. Then go upstairs to the attic. If the bulb is warm but the light is off, switch #1 is the working one. If the light is on, switch #2 is the working one. And if the light is off and cold, switch #3 is the one that works.