The World Needs More Ninjas

Here’s a neat little puzzle from Popular Science (via Boing Boing) to get your brain cranked up for the day.

Click below the fold to get an answer.

Answer:

225 factors into 5, 5, 3, 3 (and 1, of course). Thus, the ways in which it can be factored into three numbers are:

225 + 1 + 1 = 227
9 + 5 + 5 = 19
75 + 3 + 1 = 79
25 + 9 + 1 = 35
45 + 5 + 1 = 51
15 + 5 + 3 = 23
25 + 3 + 3 = 31
15 + 15 + 1 = 31

The part I got stuck on was what the house number has to do with the problem. Is it a red herring? Is there some information left out of the puzzle (e.g., it’s even or odd)?

But, the fact that the census taker has to ask, “Are you the eldest?” means that the sum of the ages is ambiguous. The only sets that meet this criteria are (25, 3, 3) and (15, 15, 1), both of which sum to 31. By determining that there is an eldest, then the answer must be (25, 3, 3).

Though, I guess this assumes that the eldest is not a twin, in which case, technically one of the twins is the eldest even though they are the same age in terms of years. Even without this technicality, it seems like “Are you the eldest?” could be answered in the affirmative by one of the 15-year-olds meaning, “Yes, I am one of the eldest in the house.”

Comments?