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Tell someone to pick a positive integer, double it, add $9$, multiply by $5$ and then subtract the number that person started with. Tell that person to remove any nonzero digits in any order the person wishes. Then you tell the person the digit the person removed.

Explain how this is done.

So lets say the person pick $10$

doubling: $20$

add $9$: $29$

multiply by $5$: $145$

subtract beginning number: $135$

Lets say, the person removed $3$. So the person final answer would be $15$,

so how would i be able to tell the digits a person removed. the person could have removed $3$, $1$, $5$ as well.

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  • $\begingroup$ You should have 135. Not 125. $\endgroup$
    – fleablood
    Oct 10, 2015 at 6:47
  • $\begingroup$ you are right, let me edit. $\endgroup$ Oct 10, 2015 at 6:48
  • $\begingroup$ It's crucial, as 1 + 3 + 5 = 9. $\endgroup$
    – fleablood
    Oct 10, 2015 at 6:56

1 Answer 1

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"Tell someone to pick a positive integer"

Okay, I call it N. (Example: 10)

"double it, add 9,"

2N + 9 (Example: 29

"multiply by 5"

10N + 45 (Example: 145)

"and then subtract the number that person started with."

9N + 45. (Example: 135)

This number is a multiple of nine. The digits add up to a multiple of nine. (Example: 1 + 3 + 5 = 9)

"Tell that person to remove any nonzero digits in any order the person wishes. Then you tell the person the digit the person removed."

When you remove a digit, v, the digits will no longer add up to a multiple of nine. They will add up to 9 - v.

(Example: 135, remove the 1 leaving 35: 3 + 5 = 8 = 9 -1. So I know a 1 was removed.)

(Example: 135, remove the 3 leaving 15: 1 + 5 = 6 = 9 -3. So I know a 3 was removed.)

(Example: 135, remove the 5 leaving 13: 1 + 3 = 4 = 9 -5. So I know a 5 was removed.)

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  • $\begingroup$ Great! I understand now. $\endgroup$ Oct 10, 2015 at 18:54

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