A.R.M. (kinkyturtle) wrote,
A.R.M.
kinkyturtle

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Brainteasing

I once got tripped up by a particularly diabolical "you'll feel stupid if you don't figure it out"-type brainteaser once. My dad showed it to me in a magazine. There was this Venn diagram, two overlapping circles, containing three sets of numbers, something like this:
      ____    ___
     /    \  /   \
   /   6   /\  156 \
 /  4884 /    \ 713 \
|  1771 |  535 | 278 |
| 29592 |  707 | 350 |
|    33 |  474 | 904 |
| 98089 |  212 | 127 |
 \ 64046 \    / 209 /
   \  7227 \/ 384  /
     \____/  \___/


You had to figure out the property shared by the numbers in each circle (the numbers inside the overlap, of course, had both properties).

I spotted right away that the numbers in the left circle were all palindromic (for example, 151, 27872, 99, etc.) but the right circle had me stumped. They were all three-digit numbers, but for the life of me I couldn't figure out what special relationship the three digits in each number had to each other. Was one digit the sum of the other two? No. Was one digit perhaps the bitwise logical XOR of the other two, or something like that? No. Hmm. Maybe it was a property of the number as a whole. Were they all a multiple of some common factor? No, nothing bigger than 1. Were they sums of anything interesting? Not that I could figure out.

Finally I gave up and asked my dad. What special property did the numbers in the circle on the right have?

"They all have three digits."

Yes, and?

"That's it."

THAT'S IT?! I felt... what, cheated? They all have three digits... that's on the level of a puzzle for first-graders! But the idea that it would be anything on a higher level than that was my own assumption. I was simply overthinking it. Paradoxically, I felt stupid by being too smart. :}
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