[RocketManJames]

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Unless I'm missing something>

I'd make a = 3 to square 37, so 34*40 + 9 = 1369.

Thanks Homer!

edit: Homer responded the same time I did, but I think that 34*40 + 9 (basically 34*4 + 9) is easier to do quickly in your head than 37*37.

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I think that overcounting then subtracting then re-adding might be simpler, but I could be wrong. Or, undercounting then adding then re-adding.

Examples:

37*37 = 40*40 - 2*(3*40) + 3*3 (uses 3 as the "difference" number)

42*42 = 40*40 + 2*(2*40) + 2*2 (uses 2 as the "difference" number)

In Edit: I understand that this is basically the same FOIL method as Homer's, but I think that breaking it down like this, while it requires 3 steps, is simpler due to the simpler numbers.

-RMJ