Math Fun

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1) Pick any 3-digit number. (The digits need to be different)
2) Reverse the digits. (ie. 123 becomes 321)
3) Subtract the lesser of the two from the greater. (ie. 321 - 123)
4) Reverse the digits in the result and add it to the original result.

The answer will always be 1089.

OK, I finally figured out why.

Let a 3 digit number be 100x + 10y + z
so for 123 x=1, y=2, z=3

Reverse the digits: The number becomes 100z + 10y + x

When you subtract the lesser from the greater, the thing is that the one's digit will be problematic and will need to carry a ten. The ten's digit will also need to carry a ten from the hundred's digit since the tens digit will always be the same but you borrowed one already so you need to also borrow for the tens digit.

for 123, the bigger number will be 100z + 10y +x.

x becomes x+10 since you need to carry a 1 over.

10y will temporarily become 10(y-1). But will eventually be 10(y-1+10)=10(y+9) since you carry a 1 over.

100z will become 100(z-1).

time to subtract:
100(z-1) + 10(y+9) + (x+10)
minus...
100x+10y+z
equals...
100(z-1-x) + 10(9) + (x-z+10) <-- new number for step 4.
Reverse and add
Reverse number--> 100(x-z+10) +10(9) + (z-1-x)
the sum is... 100(9) + 180 + 9=1089

That's very fascinating.

post deleted

) Pick any 3-digit number. (The digits need to be different)
645
2) Reverse the digits. (ie. 123 becomes 321)

546
3) Subtract the lesser of the two from the greater. (ie. 321 - 123)

645 - 546 = 99
4) Reverse the digits in the result and add it to the original result.

99 + 99 = 198

The answer will always be 1089.


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[youtube]http://www.youtube.com/watch?v=ymWrw19srQ0[/youtube]

May not fit in with the rest but it is fun with math

jc6chan: Nice!

1)Pick any 3-digit number. (The digits need to be different)
999
2) Reverse the digits. (ie. 123 becomes 321)

999
3) Subtract the lesser of the two from the greater. (ie. 321 - 123)

999-999 = 000 (there is no lesser in this case...)
4) Reverse the digits in the result and add it to the original result.

000 + 000 = 000

The answer will always be 1089, except for when you pick a symmetrical number (how was this called, I know for words it's palindrome...).