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.

I considered "no restrictions" to indicate we could create expressions:

Two matches:  Take two matches from the 3 which becomes a 7.  Place these as a carat which indicates an exponent after the 8:

8^2097 ≈ 6*10^1893
this is pretty large.

on second thought make the two matches an 11 to the lower left of 82097 so it becomes an exponent meaning
11^82097 ≈ 1.6*10^85495
which is even bigger.

Silly me.  Take the matches from the 8 and 9:
11^92033 ≈ 3.1*10^95842

For 3 matches take one from the 8 and two from the 3 and you can do a similar trick:
111^92097 ≈ 1.3*10^188368

Edited on January 22, 2014, 2:18 pm

Posted by Jer on 2014-01-22 14:11:12