ok thanks I get it.

You had to use a calc for that of course. :)

10^100 mod 72 = 64 I just used the web2.0 calc for that.

So the biggest number possible will be 10^100 - 64

the smallest 2 digits will be 36 and all the rest will be 9.

9*98+9 = 891.

Ok I can see what you have done and I can see it has worked this time but

I question if it would work everytime.

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I am just thinking out loud now.

You have found the biggest number, but I am nost so sure that the biggest number would always have the greatest sum of the digits for a question like this.

I mean I can see that it __has__ to work for this particular example because

the 2 smallest have to add up to 9, or

the 3 smallest have to add to 18 or

the 4 smallest have to add to 27 etc

And of course those small numbers can be placed anyway, they do not have to have the smallest place value.

but for other examples.......not so sure.

eg

997>989 however 9+9+7<9+8+9

**I do like your logic though - thanks for sharing it :)**