Need a help for my book

Hi, folks!

I would like to present you one cryptograph (kind of alphametics). It's Croatian, and I believe world record - three terms with 12 letters.

P I S M O S I S T O K A ('Letter from east' - title of novel) P R O K R S T A R I T I (to cruise) S T A R O K A T O L I K (Old Catholic)

Code: 7,0,8,2,4,9,3 - 9,5,6,1,3 gives additional term.

Solution: Tropska klima - tropical clime (T=7, R=0, etc.)

2 6 4 1 8 4 6 4 7 8 9 3 2 0 8 9 0 4 7 3 0 6 7 6 4 7 3 0 8 9 3 7 8 5 6 9

Can you make a work with three 13-letters terms?

Cheers!

Zoran Radisavljevic Novi Sad, Serbia

P.S. Task is really hard and I'll understand if it's beyond your power. I hope that somebody can send me few works on English with length 9-10. Thanks in advance.

One English alphametic with 10-letter words is SCRAPPIEST + CONCRETION = TRANSPOSES

I haven't found any 11's or 12's yet, but I'm working on it.

Robert Israel This e-mail address is being protected from spam bots, you need JavaScript enabled to view it Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada

: SCRAPPIEST + CONCRETION = TRANSPOSES : What does concretion mean? It's not in my dictionary. (Is it to bring something to a point at which it is solid or fixed?)

Thanks, Robert. In this type of puzzle you also must find final solution (term which contains all letters at least once, like TROPSKA KLIMA in my example). With AEIOCNPRST one possibility for final solution is APPRECIATIONS.

Cheers, Zoran

P.S. My brother lives in Vancouver!!

Here's one with 11-letter words:

REINTERPRET + SMITHSONITE = PRONENESSES

And if you want a word with all these letters, MENTORSHIP will do.

Robert Israel This e-mail address is being protected from spam bots, you need JavaScript enabled to view it Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada

I'm interested to know how you're finding these - are you just brute-forcing it? I haven't tried, but I'd have expected it to be a very long process! Although, of course, as the length of the words increases it must become increasingly difficult to find three words using only 10 different letters.

Semi-brute force. Start with a list of all 11-letter English words (extracted from the enable1 word list). Randomly choose three words x,y,z (making sure the total number of different letters in them is at most 10), and solve the alphametics x+y=z, x+z=y, and y+z=x. Repeat until successful. It takes lots of tries, of course: the probability of success in a given (11+11=11 letter) alphametic is something like 10!/(2*10^11) or about 1.8*10^(-5) (the factor 1/2 comes because you don't want a carry from the leading column). And for 12 letters the probability is divided by 10 again, so it'll need a lot of computing.

Robert Israel This e-mail address is being protected from spam bots, you need JavaScript enabled to view it Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada

Here are three with 12 letters:

orbitelariae + veritability = trilaterally (abortively) coapprentice + reconception = acronarcotic (acetopyrin) paratartaric + pyrotartaric = preintention (acetopyrin)