Friday, October 29

Solutions to Yesterday's Puzzles

If you're not ready for the answers, stop reading now!

Find all the sets of 3 factors of 72. Here they are: (1, 2, 36), (1, 3, 24), (1, 4, 18), (1, 6, 12), (1, 8, 9), (2, 2, 18), (2, 3, 12), (2, 4, 9), (2, 6, 6), (3, 3, 8), (3, 4, 6), and the highly improbable but theoretically possible (1,1, 72).

Since the guest does this and still needs one more piece of information, you know that there is more than one set of numbers that totals the guest's house number. So you can eliminate all sets that have unique totals. This leaves you with (2,6,6) and (3,3,8) which both total 14.

The hosts ice cream flavor clue tells you that there is one oldest child. That eliminates the set (2,6,6) and leaves only (3,3,8). The oldest child, then, is 8.

Now, on to the mind reading puzzle. If do the initial math problem often enough (adding the two digits of a two digit number and subtracting their total from the number itself), you will notice a pattern--the result is always a multiple of 9. If you look at the number chart on the game, all the multiples of 9 always have an identical symbol, and that's the symbol that shows up when the game "reads your mind." That particular symbol changes each time the game is reset.

[Update: Scott McClare (a.k.a The Crusty Curmudgeon, f.k.a The P of U, has posted in the comments the mathmatical proof that when you add the two digits of a two digit number and subtact their total from the number itself you get a multiple of 9, namely the product of 9 and the tens digit.]
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