Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Hundred Sum and Prime Puzzle

  1. Aug 3, 2009 #1
    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.
     
  2. jcsd
  3. Aug 3, 2009 #2
    My solution to it:
    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Similar Discussions: Hundred Sum and Prime Puzzle
  1. Hundred Year's War (Replies: 0)

  2. A puzzle (Replies: 31)

Loading...