Question 758113: When a number is divided by 10 it leaves a remainder of 9 , when divided by 9 it leaves a remainder of 8 down to where when divided by 2 it leaves a remainder of 1. Find the number.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The smallest number that has a remainder of 9 when divided by 10, a remainder of 8 when divided by 9, and a remainder of 1 when divided by 2 is  .
A number that divided by 10 leaves a remainder of 9 must end in 9, and all numbers ending in 9 are odd (not even), so that they leave a remainder of 1 when divided by 2 is .
The smallest number ending in 9 that leaves a remainder of 8 when divided by 9 is . There are larger numbers that satisfy the same conditions (179, 269, 359, 449, 539, 629, 719, 809, 899, 989, 1079, 1169, ... 1889, etc).
HOW DO I KNOW?
The remainder of a number when divided by 9 is the sum of the sum (add as many times as needed) of its digits. If you have too many digits, there is a trick to make things easier. The easier way to add is discarding any 9 you get as you are adding. For example 182736452 divided by 9 has a remainder of 2.
1+8+2+7+3+6+4+5+2=38, then 3+8=11, then 1+1=2
I figure it an easier way, because as I add 1+8=9, I discard the 9; then I add 2+7=9, and discard again, and repeat with 3+6=9 and 4+5=9, to find 2 as the sum of the sum of the sum of the digits of 182736452.
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