perplexus.info :: Numbers : Mindreader

Mindreader (Posted on 2004-03-11)

Pick any number with at least three different digits. Jumble the digits however you want to create a different number. Take these two numbers and find their difference. Their difference is your new number. Pick a non-zero digit in your new number and remove it. Give me the rest of the digits in any order you please. From this, I can work out what digit you removed.

How do I find your digit? Why does this work? Prove it.

The idea for this puzzle was taken from a mindreading program here.

Submitted by Tristan

Rating: 2.6667 (6 votes)

Solution: (Hide)

The sum of the digits of your new number is always a multiple of nine. Since the digit you picked is not a zero, I can easily tell what it is from the sum of the digits you gave me.
Here’s a proof. Since I sum up all the digits in the end, it doesn't matter that you mixed up the digits. Every digit is added and subtracted once.
The only exception is when you carry a one. For each one you carry, you add 10 to one digit and subtract 1 from another. The sum of the digits thus gets 9 more for each one that was carried. Therefore, the sum is always a multiple of 9.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: proof	DJ	2004-03-13 02:44:59
proof	ramu	2004-03-11 21:12:56
I forgot the "proof" part	TomM	2004-03-11 11:32:39
No Subject	TomM	2004-03-11 11:15:02

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