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Number machine problem 2 (Posted on 2014-12-02) Difficulty: 2 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.

Show that for any number a, there is a number x such that x gives ax.

  Submitted by Math Man    
Rating: 3.0000 (2 votes)
Solution: (Hide)
1a21 gives a21, so 21a21 gives a21a21. Let x=21a21. Then, x gives ax.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some Thoughtspossible solutionbroll2014-12-04 01:26:07
General remarks Ady TZIDON2014-12-02 08:06:55
General remarks Ady TZIDON2014-12-02 08:06:54
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