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Number machine problem 1 (Posted on 2003-06-08) Difficulty: 1 of 5
I have a number machine. I say x gives y if when x goes in, y comes out. For any numbers x and y, by "xy" I mean x followed by y. Here are my two rules.

1x gives x.
For example, 13 gives 3.
If x gives y, then 2x gives yy.
For example, 213 gives 33 since 13 gives 3.

What is a number that gives itself?

See The Solution Submitted by Tim Axoy    
Rating: 3.7000 (10 votes)

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Solution My Solution | Comment 5 of 12 |
(In reply to re(3): Solution by Gamer)

Since 1x gives x, 121 gives 21, which is not itself (121 is not 21).

However, since when x gives y, then 2x gives yy, let 121 be the x and 21 be the y (as one gives the other per the first paragraph), then 2121 gives 2121, that is itself, as 2121 is indeed 2121.
  Posted by Charlie on 2003-06-08 10:35:49

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