Two Classic Puzzlers from Cartalk

Puzzler 1:

Every two-digit number can be represented as AB, where B is the ones digit and A is the tens digit. Right? So for example the number 43, A is 4 and B is 3.

Imagine then that you took this two-digit number and you squared it, AB x AB, and when you did that the result was a three-digit number, CAB.

Here’s the question: What’s the value of C? So, for example if AB is 43, CAB might be 943. Of course this is a totally bogus answer, but you get the idea.

So again, what is the value of C, so that AB(squared)= CAB?

(spoiler – answer is here.)

Puzzler 2:

This is from my fuzzy math series. It was sent in by Dave Atkins. On a recent Saturday afternoon, I saw a boy and his mother at the neighborhood diner where I often go for lunch. From my vantage point I could see they were working on some arithmetic problems. The problems seemed simple enough and the kid was getting all the correct answers. For example, the first one was 25 + 8 and he wrote down 33. And the next one was 12 + 5 and he wrote down 17. The next was 35 + 13 and he wrote 48. Then his mother posed the last two problems. 45 – 8. The boy said 47 but I thought the answer was 37. The next one was 42 + 15. The boy said 43. I thought it should have been 57. His mother accepted both of those answers. When I saw how the kid was dressed, I did too. What was going on?

(spoiler – answer is here.)

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