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Maximizing Matches Model (Posted on 2014-01-22) Difficulty: 3 of 5
A five digit number 82093, constructed by 29 matches looks like this:


  _    _    _    _    _ 
 |_|   _|  | |  |_|   _|
 |_|  |_   |_|   _|   _|


You are requested to make this number as big as possible by moving only two matches.

What is the maximum value and how is it achieved?

What would be your answer if 3 matches were allowed to be relocated?

Be creative - no restrictions re your answers.

See The Solution Submitted by Ady TZIDON    
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Some Thoughts First attempts | Comment 2 of 16 |
It's tough to get bigger than big exponents, so my first thought is to use two matches to make a carat. The largest result I've come up with is by taking two matches from the 3 to create 820^97, or roughly 4.365*10^282.

With three matches we can go *really* big. Take one match from the 8 to make it a 9, and again take two matches from the 3 to make it a 7. Use two matches to make a carat, and the remaining match to make the 0 into an 8. Result: 92^897, or 3.294*10^1761.

EDIT: If I wanted to get extra creative with my exponents, I would take the same three matches from my second example and snap them in half to create little superscript 7s. 92097^777 is a mighty large number indeed (1.655*10^3857).

Edited on January 22, 2014, 2:08 pm
  Posted by Jyqm on 2014-01-22 13:59:45

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