Hundred Sum and Prime Puzzle


by K Sengupta
Tags: prime, puzzle
K Sengupta
K Sengupta is offline
#1
Aug3-09, 01:21 AM
P: 110
Substitute each of the capital letters by a different digit from 1 to 9 to satisfy this cryptarithmetic equation:

(P*Q)/R + (S*T*U)/V + W*X = 100, where the 2-digit number WR is prime.
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Edgardo
Edgardo is offline
#2
Aug3-09, 05:48 AM
P: 685
My solution to it:
Spoiler

In total there are 36 solutions:
p=4 q=8 r=1 s=2 t=3 u=5 v=6 w=7 x=9 p=100.0 wr=71 counter=1
p=4 q=8 r=1 s=2 t=5 u=3 v=6 w=7 x=9 p=100.0 wr=71 counter=2
p=4 q=8 r=1 s=3 t=2 u=5 v=6 w=7 x=9 p=100.0 wr=71 counter=3
p=4 q=8 r=1 s=3 t=5 u=2 v=6 w=7 x=9 p=100.0 wr=71 counter=4
p=4 q=8 r=1 s=5 t=2 u=3 v=6 w=7 x=9 p=100.0 wr=71 counter=5
p=4 q=8 r=1 s=5 t=3 u=2 v=6 w=7 x=9 p=100.0 wr=71 counter=6
p=7 q=9 r=1 s=2 t=3 u=5 v=6 w=4 x=8 p=100.0 wr=41 counter=7
p=7 q=9 r=1 s=2 t=5 u=3 v=6 w=4 x=8 p=100.0 wr=41 counter=8
p=7 q=9 r=1 s=3 t=2 u=5 v=6 w=4 x=8 p=100.0 wr=41 counter=9
p=7 q=9 r=1 s=3 t=5 u=2 v=6 w=4 x=8 p=100.0 wr=41 counter=10
p=7 q=9 r=1 s=5 t=2 u=3 v=6 w=4 x=8 p=100.0 wr=41 counter=11
p=7 q=9 r=1 s=5 t=3 u=2 v=6 w=4 x=8 p=100.0 wr=41 counter=12
p=8 q=4 r=1 s=2 t=3 u=5 v=6 w=7 x=9 p=100.0 wr=71 counter=13
p=8 q=4 r=1 s=2 t=5 u=3 v=6 w=7 x=9 p=100.0 wr=71 counter=14
p=8 q=4 r=1 s=3 t=2 u=5 v=6 w=7 x=9 p=100.0 wr=71 counter=15
p=8 q=4 r=1 s=3 t=5 u=2 v=6 w=7 x=9 p=100.0 wr=71 counter=16
p=8 q=4 r=1 s=5 t=2 u=3 v=6 w=7 x=9 p=100.0 wr=71 counter=17
p=8 q=4 r=1 s=5 t=3 u=2 v=6 w=7 x=9 p=100.0 wr=71 counter=18
p=8 q=9 r=3 s=4 t=5 u=7 v=2 w=1 x=6 p=100.0 wr=13 counter=19
p=8 q=9 r=3 s=4 t=7 u=5 v=2 w=1 x=6 p=100.0 wr=13 counter=20
p=8 q=9 r=3 s=5 t=4 u=7 v=2 w=1 x=6 p=100.0 wr=13 counter=21
p=8 q=9 r=3 s=5 t=7 u=4 v=2 w=1 x=6 p=100.0 wr=13 counter=22
p=8 q=9 r=3 s=7 t=4 u=5 v=2 w=1 x=6 p=100.0 wr=13 counter=23
p=8 q=9 r=3 s=7 t=5 u=4 v=2 w=1 x=6 p=100.0 wr=13 counter=24
p=9 q=7 r=1 s=2 t=3 u=5 v=6 w=4 x=8 p=100.0 wr=41 counter=25
p=9 q=7 r=1 s=2 t=5 u=3 v=6 w=4 x=8 p=100.0 wr=41 counter=26
p=9 q=7 r=1 s=3 t=2 u=5 v=6 w=4 x=8 p=100.0 wr=41 counter=27
p=9 q=7 r=1 s=3 t=5 u=2 v=6 w=4 x=8 p=100.0 wr=41 counter=28
p=9 q=7 r=1 s=5 t=2 u=3 v=6 w=4 x=8 p=100.0 wr=41 counter=29
p=9 q=7 r=1 s=5 t=3 u=2 v=6 w=4 x=8 p=100.0 wr=41 counter=30
p=9 q=8 r=3 s=4 t=5 u=7 v=2 w=1 x=6 p=100.0 wr=13 counter=31
p=9 q=8 r=3 s=4 t=7 u=5 v=2 w=1 x=6 p=100.0 wr=13 counter=32
p=9 q=8 r=3 s=5 t=4 u=7 v=2 w=1 x=6 p=100.0 wr=13 counter=33
p=9 q=8 r=3 s=5 t=7 u=4 v=2 w=1 x=6 p=100.0 wr=13 counter=34
p=9 q=8 r=3 s=7 t=4 u=5 v=2 w=1 x=6 p=100.0 wr=13 counter=35
p=9 q=8 r=3 s=7 t=5 u=4 v=2 w=1 x=6 p=100.0 wr=13 counter=36


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