[Racoon]

Heres a Math trick someone showed me the other day.

1) Take any 3 digit number, But the first and third number Cannot be the same.

853

2) reverse the order and subtract
853
-358
=495

3) reverse the answer and then add it
495
+ 594
=1089
The Answer always equals 1089!

try again: 921
-129
= 792

792+297= 1089!
Amazing huh?

Got an explanation for this?
Have any other Math Tricks of your own?

[C1ay]

Racoon said:

Heres a Math trick someone showed me the other day.

1) Take any 3 digit number, But the first and third number Cannot be the same.

Try it with 102

[Racoon]

You're a dirty dog clay!
It didn't take you long to debunk my trickery!

[C1ay]

It's because of an exception in another trick I know of.

Ask someone to think of a 3 digit number where none of the digits are the same.
Have them reverse the number and subtract the smaller from the larger.
Have them tell you the last digit of the answer and you tell them the whole answer.

This sequence will always yield an answer where the middle digit is 9 and the sum of the first and last digits is 9. The only exception will be when they select an initial three digit number where the first and last digits only differ by 1. In this case the final answer will be 99.

[CraigD]

Racoon said:

Take any 3 digit number…
Got an explanation for this?

A little bit of simple algebra can explain this, and many other similar, tricks. Here goes:

• Take any 3 digit number, But the first and third number Cannot be the same.
  Let’s represent our 3 digit number as 100A +10B +C
  
• reverse the order and subtract
  Gives 100A +10B +C – (100C +10B –A) =
  99(A -C)
  Now a little intuition is needed. Lets substitute “D +1” for “A –C”, rewrite the number as
  99(D +1)
  and rearrange this into
  99D + 99 =
  100D -D +90 +9 =
  100D +10(9) +(9 -D)
  
• reverse the answer and then add it
  Gives 100D +90 +(9 -D) +(100(9 -D) +90 +D),
  which rearranges into
  100(D +(9 -D)) +180 +(9 - D +D) =
  100(9) +180 + 9 =
  1089

Back in my remedial math teaching days, I used to respond to my students who asked "what will I ever use algebra for?" by telling them it could keep them from loosing money to trick barroom bets - provided they remember to sneak off to the bathroom with a paper and pencil whenever they're offered one )

[Qfwfq]

Maybe it can be said more simply. The first step clearly doesn't depend on the central digit and it will be 99 times the difference between the left and the right digit. This is negative in C1ay's case.

The three digit reverse of 099 is 990 and their sum is 1089 (-1089 in C1ay's case). Each time you add 99 to the first, the second is decreased by 99. Why? The reason for this is the trickiest part, you are adding 990 with a backward carry rule, which in the case of the digit 9 amounts to the borrow rule for subtracting 9 from the digit to the right, because both these things decrease the one digit and increase the other.

99 + 99 reversed is 891 = 990 - 99 etc.

[Racoon]

Thanks for breaking it down for me CraigD.

Math is logical, even when parlor tricks and games are involved.

Anyone have any quirky and fun math tricks?

[CraigD]

chendoh said:

… Here's one that I enjoyed, back in 2002.

I've been trying to get it to work for succeeding years by changing numbers 2,3,4,
and 5, mostly #5 with no luck. maybe with a little help from our resident math wizards.…

This is an easy one to figure out with some simple algebra. Just write the 6 instructions as an expression
50(2n+5) +1752 –y
, where n is the number from step 1, and y is your birth year
, simplify it to
100n +2002 –y
. 2002 –y is just the usual formula for your age in 2002. As long as you’re under 100 years old, and n is from 1 to 9, you’ll get a 3-digit number, where the last 2 are your age.

You can make the problem work for any year by changing the step 5 numbers to the year -250 and year -249, or you can change the numbers in all the steps, as long as the step 2 and step 4 number multiplied are 100, and the step 5 number is the current year –(step 3 number)*(step 4 number). For example
20(5n +17) +1666 –y
translates into
1) pick a number from 1 to 9
2) multiply it by 5
3) add 17 to it
4) multiply by 20
5) add 1666 if you’ve already had your birthday, 1665 if you haven’t
6) subtract the four digit year that you were born.

With a little algebra, you can create countless tricks like this

[lawcat]

c1ay said:

try it with 102

Edit: Oops! Did not se Qfw's post above.

[sculican]

Try the number 102 with this trick