Math CentralQuandaries & Queries


Question from Peggy, a parent:

I'm sorry. I forgot to include the hint to the problem I sent earlier.

The problem was: Number a = 111...111 formed by 2003 1's. Find the sum of the digits of the number 2003 * a.

The hint that was included states: Try column multiplication to find a pattern.

Thanks so much for all the help. I'm sure this is a LOT easier than I think it is, but I just can't seem to even begin to find a way to solve it.

Hi Peggy,

I would try with a a smaller number, say a = 11111. Calculate 2003 × a by hand, without a calculator. Do the same with a = 111111. Can you now see what the value of 2003 × a would be if a had 2003 ones rather than 5 or 6? What is the sum of the digits?


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