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Very simple but tricky question

n is a 2 digit number
n is divided by 10, remainder is 9
n divided by 9, remainder is 8
what is n?

I tried everything from simultaneous equations to even matrices which is stupid. Is there any way of finding n without trial and improvement?
Original post by Elmi
n is a 2 digit number
n is divided by 10, remainder is 9
n divided by 9, remainder is 8
what is n?

I tried everything from simultaneous equations to even matrices which is stupid. Is there any way of finding n without trial and improvement?




I just thought that because n/10 leaves a remainder of 9, you know that the number must end in a 9, and because n/9 leaves a remainder of 8, the number must be 8 bigger than a multiple of 9, and the only number this could mean is 89?
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Elmi
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Original post by Brandon_97
I just thought that because n/10 leaves a remainder of 9, you know that the number must end in a 9, and because n/9 leaves a remainder of 8, the number must be 8 bigger than a multiple of 9, and the only number this could mean is 89?


After so much thinking it is that simple.

I thought n/10=x+9 and n/9=y+8 but there seem to be no relationship between both equations
Your number takes the form
9+10x or 8+9y
now its fairly easy to brute force and see that its a number ending in 9, 8 more than a multiple of 9.
using these two facts its easy to see that the only multiple of 9 which is under 100 and adding an 8 to will make a number ending in 9 is 81 thus our number is 89.
Now a slightly more advanced way of doing it is using modular arithmetic.

nmod(10)=9
nmod(9)=8

n+1=0mod(9*10)
n=89

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