Puzzle
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Ponder This Challenge - April 2013 - Sum of fractions

Ponder This Challenge:

This month's challenge is based on a suggestion by Kerry M. Soileau (thanks!).

One can replace the letters in the expression I/M = B/A+C/K with different digits from 1 to 6 to form a valid equation. For example: 5/6 = 2/4+1/3. Substituting back letters to digits, using the same solution ACK.IBM is 413.526.

The problem: Replace the letters with different digits such that D/O+N/T = P/E+R/I+S/H and send us PONDER.THIS translated back to a number.

We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com

Solution

  • This month's challenge was quite easy - even checking all 10! possibilities is feasible, and noting the symmetries and the fact that 5 and 7 cannot be in the denominator makes it even simpler.

    Another way to solve it is to take the example we gave 5/6 = 2/4 + 1/3 replace 2/4 with 1/4+2/8; 1/3 with 3/9; and 5/6 with 5/6+0/7 and get 0/7 + 5/6 = 1/4 + 2/8 + 3/9 which translates to PONDER.THIS = 175042.6983

Solvers

  • Marla Slusky (03/29/2013 04:48 PM EDT)
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