 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Remainder: Part 1 (Posted on 2006-03-20) A hundred digit number is formed by writing the first few natural numbers in front of each other as follows:

12345678910111213141516171819…………………

Find the remainders when this number is divided by each of the numbers from 1 to 20.

 No Solution Yet Submitted by Ravi Raja Rating: 2.5000 (2 votes) Comments: ( Back to comment list | You must be logged in to post comments.) A start (partial solution) | Comment 1 of 6

Well, ok, here's what I could do with a pen and an 8-digit pocket calculator:

The hundred digit number will end with ...5253545 (right in the middle of 55).

`divisor remainder reason------- --------- ------   1        0     obvious   2        1     number ends in 5   3        2     digits sum to 5   4        1     last two digits = 45   5        0     number ends in 5   6        5     remainder when divided by 2 = 1, and by 3 = 2;        8        1     last three digits = 545   9        5     digits sum to 5  10        5     number ends in 5  11        1     sum of 1st, 3rd, etc digits - sum of 2nd, 4th, etc.  12        5     remainder when divided by 3 = 2, and by 4 = 1    15        5     ends in 5, remainder when divided by 3 = 2  16        9     last four digits = 3545`
`  18        5     remainder when divided by 2 = 1, by 9 = 5    20        5     last two digits = 45`
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 Posted by tomarken on 2006-03-20 11:12:33 Please log in:

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