To determine whether a number is divisible by 4, you look at its last 2 digits. The only 2-digit numbers that have all their numbers the same and are divisible by 4 are 44 and 88.

So whatever number you pick will be made up of a load of 4's or a load of 8's and will have to be divisible by 7. And in fact, since 444... is a factor of 888..., we can get away with only trying chains of 8's.

Let's try some then.

8/7 = 1.14... NO

88/7 = 12.57... NO

888/7 = 126.86... NO

8888/7 = 1269.71... NO

88888/7 = 12698.29... NO

888888/7 = 126984. Success!

And as the quotient is even, we can tell that 444444 will also work.

So the answer is 444444/28 = 15873 times.

Either your daughter is very intelligent or she pressed the equals button on her calculator a lot of times.

]]>Lisa, went shopping for tiles at the local shop the other day. The tiles were on sale for only 28 dollars each.

However, she got it in her head that, for good luck, the total amount of dollars she must spend must be a number where all of the digits are the same.

]]>this one satifies it, doesnt it?

and this?

of course it's just about keeping the upper part(so sorry, don't the english term.. "tÃ¦ller" in danish ) made of the same numbers. 111,33333,444444,5555555.... They should all work ]]>

0*28 = 0, and every digit of the number 0 is the same

]]>The proof wouldn't be too hard. First prove that 28^n is even. That is, it ends in a 0, 2, 4, 6, or 8. Then prove there must be at least one odd number in it. That will be a bit more tricky.

]]>I have a feeling Ricky's right either way though. But I have no idea how it could be proved.

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