DJ! At least, he got the answer that agreed with mine, perhaps because he was the only one who interpreted the song the same way I did. (Technically, yes, the little one isn't "left out" when the ants go marching one by one, but he always stops so he always gets left behind and has to hurry to catch up.)
The easiest way I can think of to set up the problem is to mentally line up all the numbers involved (10)(9)(8)(7)(6)(5)(4)(3)(2). You must include 7, because no other number under 10 is divisible by 7. If you keep 9 and 8, you don't need 6, because any number divisible by 9 and 8 will be divisible by 6. You can eliminate 4, 3, and 2 for the same reason. You already have a 2 in 8, so you don't need it in 10--just keep the 5.
That leaves 9x8x7x5=2520, plus the little one.
2 comments:
I demand a recount! You asked for the SMALLEST number of ants, not the number you were thinking of. I will concede that 100 is wrong. My final answer is 21, and I have posted a full explanation elsewhere.
(QOC, thanks for the much-needed diversion!)
OK, I suppose I should have specified that I was thinking of the same group of ants marching each time, instead of them calling in reinforcements as the numbers grew.
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