# Riddles, enigmas and such

**URL:** <https://boards.straightdope.com/t/riddles-enigmas-and-such/913539>\
**Category:** Thread Games\
**Created:** [June 28, 2020, 4:50pm UTC](https://boards.straightdope.com/t/riddles-enigmas-and-such/913539 "2020-06-28T16:50:36Z")\
**Posts on this page:** 2\
**Page:** 5

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**Author:** ![lobotomyboy63](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lobotomyboy63/32/2900_2.png) [@lobotomyboy63](https://boards.straightdope.com/u/lobotomyboy63)\
**Post date:** [January 28, 2022, 2:16am UTC](https://boards.straightdope.com/t/riddles-enigmas-and-such/913539/82 "2022-01-28T02:16:35Z")

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@Gyrate’s spoiler

Since the numbers are AA, BB, and CC we could rewrite as 10A + A, 10B + B, and 10C + C. That’s 11(A+B+C) so you know ABC has to be a multiple of 11. Considering that it’s over 100, the even multiples 121, 132, 143, and so on show that B-A=C. As you say, AA + BB =110 so the last digit will be C. And as you say the number can’t be over 300, since 99 + 99 + 99 is only 297. If we try the 2 as A and 8 as B, then C would be 6. But 22 + 88 + 66 isn’t 286. That leaves A=1, so B must be 9, and C must be 8. The other solution: -1, -9, -8.

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**Author:** ![Biotop](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/biotop/32/321_2.png) [@Biotop](https://boards.straightdope.com/u/Biotop)\
**Post date:** [January 28, 2022, 3:55am UTC](https://boards.straightdope.com/t/riddles-enigmas-and-such/913539/83 "2022-01-28T03:55:58Z")

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Good job. Found that math riddle at [Futility Closet](https://www.futilitycloset.com)

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