This week’s puzzle might take a little bit of math to solve, but it shouldn’t be too hard if you passed basic math classes. You’ll also need to know what square numbers mean…

I recommend grabbing a piece of paper and a pencil, and probably a calculator. Always good to have those around.

Many numbers, particlarly in the lower orders, can make a good claim for being of particular interest. It is in the realm of square numbers, that 48 is of special curiosity. If you add 1 to it, you get a square number

[48 + 1 = 49 = 7 x 7], and if instead you halve it and add 1 to the result, you get a different square number [48/2 = 24) + 1 = 25 = 5 x 5]. Individually, the two conditions are trivially common, but taken together this way, they are less so.

In fact, 48 is the smallest number to satisfy both conditions. Can you find the next smallest to do so?

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THE ANSWER IS BELOW

1680 is the next lowest number that fits these conditions.

1680 + 1 = 1681 = 41 x 41

(1680/2 = 840) + 1 = 841 = 29 x 29

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