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Much of few is many (Posted on 2016-04-28) Difficulty: 3 of 5
Much of few is many, at least in Spanish:

15*POCO=MUCHO

Try to solve analytically.

Source: MIT Technology Review.

No Solution Yet Submitted by Ady TZIDON    
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Solution Full solution | Comment 1 of 2
O must be 0 or 5.

Suppose O=0
We can ignore the terminal zeros so that
15*P0C=MUCH
Now H must be 5 and M is odd
15*P0C=MUC5
But now we require 15*0C ends in C5 which means C=1
15*P01=MU15
With the lack of carries, 15*P=MU but both 0 and 5 are taken so there's no choices for U.
So O is not 0.

Suppose O=5
15*P5C5=MUCH5
If C is odd, H=2.  If C is even H=7
If H=2, it can easily be shown that no choice of C in POCO puts the same C in MUCHO.
If H=7, the only choice for C that works is C=9.

15*P595=MU975
P must be 6 or less.  Checking each gives a single solution:

15*4595=68925

  Posted by Jer on 2016-04-28 11:59:32
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