[Guest]

I saw this "magic" trick once as a 7up ad. I thought I'd recreate it as word problem.

Arun asks Steve to pick any big number (say 3, 4 or 5 digits long).

Arun then asks Steve to rearrange the digits of the number and find the difference.

Arun asks him to finally circle any digit in the difference, but not a 0 because 0's already a circle, and to tell him the remaining number without the circled digit.

Steve does and tells him "307".

Arun thinks for a second and then says "Ah, the digit you circled was __."

What was the digit and how did Arun know?

[Guest]

I saw this "magic" trick once as a 7up ad. I thought I'd recreate it as word problem.

Arun asks Steve to pick any big number (say 3, 4 or 5 digits long).

Arun then asks Steve to rearrange the digits of the number and find the difference.

Arun asks him to finally circle any digit in the difference, but not a 0 because 0's already a circle, and to tell him the remaining number without the circled digit.

Steve does and tells him "307".

Arun thinks for a second and then says "Ah, the digit you circled was __."

What was the digit and how did Arun know?

8. The difference after rearranging the digits will always be divisible by 9.

For any number to be divisible by 9, the sum of all the digits should be divisible by 9. Now the digits, 3,0, 7 add up to 10 and if 8 is added, the sum becomes 18.

[Guest]

8. The difference after rearranging the digits will always be divisible by 9.

For any number to be divisible by 9, the sum of all the digits should be divisible by 9. Now the digits, 3,0, 7 add up to 10 and if 8 is added, the sum becomes 18.

There may be some condition required for this to work missing besides, "any big number". While trying to understand how the trick works, I tried a simple number, 1111. I circled a 1, rearranged the other digits... as best I could... and came up with 111. I'm not sure what "difference" is referred to in the solution, but tried "1111-111" (original-rearranged), and "111-111" (original uncircled-rearranged), and couldn't come up with anything to match what I'd circled when adding digits up to nine.

What am I missing?

[Guest]

There may be some condition required for this to work missing besides, "any big number". While trying to understand how the trick works, I tried a simple number, 1111. I circled a 1, rearranged the other digits... as best I could... and came up with 111. I'm not sure what "difference" is referred to in the solution, but tried "1111-111" (original-rearranged), and "111-111" (original uncircled-rearranged), and couldn't come up with anything to match what I'd circled when adding digits up to nine.

What am I missing?

I think you misunderstood the difference that has to be considered. Let me explain by an example. You pick a four digit number say 1234.. Now re-arrange the digits and you may get say 3421. Now find the differnce of 1234 and 3421. The result is 2187. The sum of the digits of this difference (2,1,8,7) will always be divisible by 9. You circle one of the digits and tell me the other 3, and I can easily tell the circled digit by subtracting the sum of these 3 from the next nearest multiple of 9.

Now consider the difference of 1234 and 4231. The result is 2997. You circle a nine and tell me the other 3 i.e is 2, 9, 7 whose sum i.e 18 is already divisible by 9. Now I can add a 0 or 9 to make it divisible by 9. But I know you didn't circle a zero. So the answer is 9.

[bonanova]

A favorite, posted here.