If each of the of the bolded letters represents uniquely a different digit in base 10 alphametic:
PY*MY = EEE
(order of answering 1. & 2. is important! )
1.What is the minimal value of E*M*P*T*Y ?
2. Now solve the alphametic.
At first glance, solving 1 without reference to starting to do 2, would have us say the minimal value is zero, if one of the factors is zero.
Based on the alphmetic, we know that only T can be zero, but since it can, then the minimal value of E*M*P*T*Y is then zero.
What can EEE be? Let's factor the possibilities:
111 = 3 * 37, not suitable for the alphametic
222 = 2 * 3 * 37; ditto
333 = 3 * 3 * 37; again the same
444 = 2 * 2 * 3 * 37; 12 * 37 doesn't have the requisite matching units digits
555 = 5 * 3 * 37; 15 * 37 also doesn't
666 = 2*3*3*37; 18 * 37 alsoo
777 = 7 * 3 * 37; likewise 21 * 37
888 = 2*2*2*3*37; 24*37, the same problem
999 = 3 * 3 * 3 * 37; aha! 27*37 = 999 is the solution to the alphametic, or of course 37*27 = 999.
This doesn't affect part 1, as T can still be zero.
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Posted by Charlie
on 2016-09-01 12:57:44 |
solution