How do I solve this number trick?? ?

Question

first you pick a 3 digit number such as 249 (you can double numbers like 232 but not triple them like 222) then scramble the number. like 492. now subtract 492 - 249= 243.<--(the bigger minus the smaller) next circle one of the digits (not zero) I circled 4. the remaining numbers are 2 and 3 or 23. okay to finish, my teacher had me tell him the remainding number, which was 23 so i said 23 and he said that the number I circled was 4. FrEaKy!!

So, we're doing this in my high school math class -----i need to know by the second of September!! PLEASE HELP!!!! i just need to know how he knew the number I circled was 4.....!!

Answer 1

The sum of the digits has the same remainder when

divided by 9 as the number itself.

That doesn&#039;t change when you scramble the digits.

The subtraction then eliminates that remainder,

so the result of the subtraction is divisible by 9.

The sum of the digits is then either 9 or 18.

The missing digit can be determined by subtracting

the total of the other digits from 9 or 18.

492 - 294 = 243  (total 9)

9 - (2+3) = 5

891 - 189 = 693 (total 18)

18 - (9+3) = 6

18 - (6+3) = 9

18 - (6+9) = 3

.

Answer 2

Hi,

492 - 249 = 243

492 - 429 = 63

801 - 108 = 693

998 - 989 = 9

951 - 159 = 792

980 - 89 = 891

The digits in the answers always add up to a multiple of 9 - either 9 or  18. So if you told me 2 digits were 2 and 3, then 2 + 3 already adds up to 5, so to have a complete total of 9, the other number is 4.



If you told me 2 digits were 7 and 9, then 7 + 9 already adds up to 16, so to have a complete total of 18, the other number is 2.

I hope that helps!! :-)

  

Answer 3

well if its a 2 digit number add the 2 digits and then sutract one thats your number but if you have a one digit number its just the same number

Answer 4

how about a clue...

the reason you can&#039;t circle a 0 is then giving the other two numbers, it would be impossible to tell if the number you circled was a 0 or a 9.

take any three digit number like you mentioned.  there are only 5 other ways to arrange those numbers.  less if  you choose two numbers the same.  do the subtraction on all five different combinations and see what is similar about all the answers.

interesting trick, but that should be enough of a hint.