perplexus.info :: Algorithms : Number machine problem 1

Number machine problem 1 (Posted on 2003-06-08)

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?

Submitted by Tim Axoy

Rating: 3.7000 (10 votes)

Solution: (Hide)

We first need to find a number i such that for any number x,ix gives xx,so ii will give ii,which is itself. Well,21 is such an i because for every number x,1x gives x,and so 21x gives xx. Therefore,2121 gives itself.
We double check:By my first rule,121 gives 21,and so by my second rule,2121 gives 2121,which is itself.

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

Subject	Author	Date
Answer	Math Man	2014-06-23 20:32:09
Puzzle Solution	K Sengupta	2008-06-05 03:25:28
answer	K Sengupta	2007-09-05 23:32:27
re: solution	Lawrence	2003-08-24 16:34:22
solution	joy	2003-06-16 17:21:54
Category Placement?	Brian Smith	2003-06-09 15:56:35
It is...	John Tate	2003-06-08 11:18:11
My Solution	Charlie	2003-06-08 10:35:49
re(3): Solution	Gamer	2003-06-08 06:56:20
re(2): Solution	Charlie	2003-06-08 05:02:57
re: Solution	Gamer	2003-06-08 04:48:26
Solution	Jun	2003-06-08 04:37:32

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