Posted by **Kara** on Sunday, October 4, 2009 at 7:10pm.

A number magician tells you: : Pick any positive integer and multiply it by 18. Delete one of the non-zero digits of the product. Tell me the sum of the remaining digits of the product and I will tell you what digit you deleted." Explain this trick.

- Math -
**Reiny**, Sunday, October 4, 2009 at 7:22pm
Based on the property that for any number multiplied by 9 the sum of the digits in the answer must be a multiple of 9

since 18 = 2x9, this still holds true.

e.g. 23x18 = 414 and 414 is divisible by 9

suppose we had deleted a 4, the sum would now be 5. How much to the next multiple of 9 ?? clearly 4, which was the number deleted.

e.g. #2 4963x18 = 89334

suppose we delete the 8, the sum of the remaining digits is 19.

What is the next multiple of 9 after 19 ?

it is 27

how far from 19 to 27 ?

8 -- which is the number we deleted.

## Answer this Question

## Related Questions

- math - Can u please help me with this..this is my sons 6th grade work and im ...
- math - Posted by nicole on Monday, September 22, 2008 at 4:32pm in response to ...
- math - Posted by nicole on Monday, September 22, 2008 at 4:32pm in response to ...
- maths - The product of the digits of a positive two-digit number exceeds the sum...
- Math - If a positive two-digit integer is divided by the sum of its digits, the ...
- math - the 2-digit # that is divisible by both the sum and the product of its ...
- Math help please - Show that one and only one out of n,n+4,n+8,n+12,n+16 is ...
- discrete math - 1)prove that if x is rational and x not equal to 0, then 1/x is ...
- pcm - Find the last three digits of the sum of all positive integers n<1000, ...
- math - While adding ten two-digit numbers the digits of one of the numbers were ...

More Related Questions