Calculator Keys Puzzle

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Problem Description

The young math professor noticed one day that this subset of his calculator's keys could be read as an equation, but not a valid one:   
But by exchanging a couple of pairs of numeric keys he could make the equation valid.  Can you find the 2 pairs of keys that he swapped?

Background & Techniques

Another puzzle from the Giant Book of Mensa Mind Challenges  book.  Click on pairs of keys until a true equation is formed.   There are 1296 ways to swap two pairs of keys, 36 ways for each pair, so 36x36=1296 ways altogether.   (There are 9 times 8 (72) choices for each pair, but since swapping a with b is identical to swapping b with a and they are both included in the 72, we must divide by 2, resulting in 36 unique pair swaps of the 9 keys).

I'll admit that I never did solve the puzzle manually in any number of swaps.  But a search of all 1296 possibilities although quite time consuming for us, is trivial for the computer.  So in addition to clicking on the keys to swap them, I added a Solve button for the lazy.   

There are about 150 lines of user code in the program, about half to handle user clicks and half for the solve search procedure.  Function CheckAns checks the keys to see if the equation is satisfied.   The keys themselves are TButton controls put into an array for easy referencing. Keys are swapped by simply exchanging their caption and tag values within the array.   I included two standard wave files in the zipped files, just incase they are missing from a particular system.   "Balloon.wav" is a fairly unobtrusive error sound when the equation after a swap is false. "Tada.wav" is the reward for a valid solution.

Running/Exploring the Program 

Suggestions for Further Explorations

Are there solutions requiring 3 or more pair swaps? 


Created: April  9, 2006

Modified: February 18, 2016


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