All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Going Arithmetic With Alphametic II (Posted on 2009-11-21) Difficulty: 3 of 5
Substitute each of the capital letters in bold by a different digit from 0 to 9 such that the sum of digits of each of POIRE, OPERA, PORTE, TAPIS, ASTRE, PATRE, LOTUS, LISTE, LOUPE and, OUTRE (in this order) constitutes ten consecutive terms of an arithmetic sequence in ascending order. It is known that none of P, O, T, A and L can be zero.

See The Solution Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Analytic solution Comment 3 of 3 |

OPERA and PORTE are consecutive and share O,P,E,R, so A+1=T

ASTRE and PATRE are consecutive and share A,T,R,E, so S+1=P

LISTE and LOUPE are consecutive, share L and E, so I+S+T+1=O+U+P
with S+1=P then I+T=O+U

LOTUS and LISTE are consecutive and share L,T,E, so O+U+1=I+E
with I+T=O+U, then T+1=E

POIRE and PORTE differ by 2 and share P,O,R,E, so I+2=T

PORTE and OUTRE differ by 7 and share O,R,T,E, so P+7=U

PATRE and LISTE differ by 2 and share T and E, so P+A+R+2=L+I+S
with S+1=P and I+1=A, then R+4=L

Now, S and P are consecutive, P+7=U
I,A,T,E are all consecutibe
and R+4=L
For all those to fit together in ten digits, the order must be one of:
1: O,S,P,R,I,A,T,E,L,U
2: S,P,R,I,A,T,E,L,U,O
3: R,S,P,O,L,I,A,T,E,U

The difference of POIRE and TAPIS should be 3:
1:POIRE=16, TAPIS=18, diff=2: NO
2:POIRE=21, TAPIS=13, diff=-8: NO
3:POIRE=18, TAPIS=21, diff=2: YES


  Posted by Brian Smith on 2009-11-21 20:32:17
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (8)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information