mind bender

[BJClark]

After reading each window, click on the boy in the
lower right corner of the picture.

2) In the last window type in your answer in the white box using the Keyboard
(there is NO cursor).

3) Watch the paper in the boy's hand. You will be amazed.

Fido Puzzle

 

[jambo]

I am utterly astonished. My wife and son also tried it and can't figure this one out.

 

[skellam]

The answer lies wrapped in the mysteries of 8th grade Algebra.

You can prove this algebraically. Let's let the bigger number be 'abc'. This breaks down to:
100a + 10b + c

The reversed number is 'cba'. This becomes:
100c + 10b + a

When you subtract, the 10b terms cancel out and you get:
99a - 99c

Since 'a' is greater than 'c' (and all digits are different), this will be a positive number. (If a and c were the same, you would end up with zero. But this is why they tell you to pick a "completely random number with all the digits different".)

You can factor out a 9:
9(11a - 11c)

So this proves that no matter what 3 digit number you pick, the result will be a multiple of 9.

The same is true for a 4 digit number 'abcd':
1000a + 100b + 10c + d
The reverse is 'dcba'
1000d + 100c + 10b + a

Subtracting:
999a + 90b - 90c - 999c

Again you can factor out a 9:
9(111a + 10b - 10c -111c)

You could actually do this with 2 digit numbers, 5 digit numbers, 6 digit numbers, etc. With 2 digit numbers, you are liable to end up with only a single digit (9), so that wouldn't be too exciting and the trick might be apparent. With more digits, you are likely to make a subtraction error and ruin the trick. So they settled on 3 or 4 digits.

As we learned in school, the digits of a multiple of 9 also add up to a multiple of 9.

So when you leave out a digit, the program can easily figure out what number is missing to make it add up to a multiple 9. For example, 1089...

If I tell the program everything but 1, the remaining digits (0,8,9) add up to 17... the next multiple of 9 is 18. The difference is 1.
Or if I pick 8, the remaining digits (1,0,9) add up to 10. The next multiple is 18 and the difference is 8.
If I pick 9, the remaining digits (1,0,8) add up to 9. The *next* multiple of 9 is 18, so the difference is 9.

Now notice they told you *not* to circle a zero (giving some excuse like "it is already a circle"). The reason they did this is that subtracting 0 or 9 will always make another multiple of 9, and it wouldn't be clear if the number that was removed was a 0 or 9. If they disallow you from picking a zero, this ambiguity goes away. Thus the program always looks for the digit that will get to the next multiple of 9.

from answers.yahoo.com

 

[jambo]

The answer lies wrapped in the mysteries of 8th grade Algebra.

You can prove this algebraically. Let's let the bigger number be 'abc'. This breaks down to:
100a + 10b + c

The reversed number is 'cba'. This becomes:
100c + 10b + a

When you subtract, the 10b terms cancel out and you get:
99a - 99c

Since 'a' is greater than 'c' (and all digits are different), this will be a positive number. (If a and c were the same, you would end up with zero. But this is why they tell you to pick a "completely random number with all the digits different".)

You can factor out a 9:
9(11a - 11c)

So this proves that no matter what 3 digit number you pick, the result will be a multiple of 9.

The same is true for a 4 digit number 'abcd':
1000a + 100b + 10c + d
The reverse is 'dcba'
1000d + 100c + 10b + a

Subtracting:
999a + 90b - 90c - 999c

Again you can factor out a 9:
9(111a + 10b - 10c -111c)

You could actually do this with 2 digit numbers, 5 digit numbers, 6 digit numbers, etc. With 2 digit numbers, you are liable to end up with only a single digit (9), so that wouldn't be too exciting and the trick might be apparent. With more digits, you are likely to make a subtraction error and ruin the trick. So they settled on 3 or 4 digits.

As we learned in school, the digits of a multiple of 9 also add up to a multiple of 9.

So when you leave out a digit, the program can easily figure out what number is missing to make it add up to a multiple 9. For example, 1089...

If I tell the program everything but 1, the remaining digits (0,8,9) add up to 17... the next multiple of 9 is 18. The difference is 1.
Or if I pick 8, the remaining digits (1,0,9) add up to 10. The next multiple is 18 and the difference is 8.
If I pick 9, the remaining digits (1,0,8) add up to 9. The *next* multiple of 9 is 18, so the difference is 9.

Now notice they told you *not* to circle a zero (giving some excuse like "it is already a circle"). The reason they did this is that subtracting 0 or 9 will always make another multiple of 9, and it wouldn't be clear if the number that was removed was a 0 or 9. If they disallow you from picking a zero, this ambiguity goes away. Thus the program always looks for the digit that will get to the next multiple of 9.

from answers.yahoo.com

That was just what I thought it was

 

[Staphlobob]

Try "666" and see what happens.