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Letter Crunching

Posted by Karl Sharman on October 23, 2010 – 8:20 am

I have a 5 letter word written in front of me. If you ask me any five letter word, I will tell you how many letters in common your word has with mine. If my word is BLACK and yours is WHITE, I will tell you 0. If my word is PLUME and yours is AMPLE I will tell you 4. Knowing that my word contains no duplicated letters, you should be able to deduce my word with only a handful of guesses or comparisons.

Then I tell you I have a list of 26 words; One for every letter of the alphabet. No duplicated letters in any words. I then take the word beginning with A and compare it to all the the other words on my list and give you the scores. I then take the word beginning with B and so on. With the exception of the X, all words are common words, so words like YURTA can be eliminated.

Your task is to find all 26 words.

Letter Grid

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  1. 1. Kevin Said:

    Hello Tom,
    Tough to answer as I am unable to read your grid even when I try enlarging. At least I think I can give you a process answer here. I would of started the process by eliminating letters from the words wherever possible using the (0) marks as eliminators. Then I would look for the words that had (5) common letters to narrow down at least one or two words which would then allow the work to flow either way from there. I think I see that there is a (5) for the (e) word under the (H) word which would lead me to believe we are dealing with words such as Earth and Heart in this situation. Then working in reverse it would becomes a matter of trial and error if the numbered grid was legible. Sorry

  2. 2. Knightmare Said:

    as i see it-the word that starts with c amd the word that starts with r and the word that starts with t all share the same 5 letters.one of the other three bmight be M.i’m stuck here.

  3. 3. Wizard of Oz Said:

    Are they all five-letter words?

  4. 4. Karl Sharman Said:

    They are all five letter words. Sorry, but I don’t know how to make the grid any bigger. I put it in as a picture as I couldn’t type it in to show correctly.

  5. 5. Wizard of Oz Said:

    Well, now that we know that all words have 5 letters we can start with those cells that have a 5 in them.
    Combinations of C, R and T all have 5s so there must be three five-letter anagrams containing these three letters and beginning with each of them in turn.

    CATER, REACT and TRACE spring to mind. So that’s three words found.

    For E and H we could have EARTH and HEART.

    For Q and S we could have QUIDS and SQUID.

    Have to go now, but that’s a start.

  6. 6. Locke Said:

    I think what Wizard of Oz posted is the key to solving this.

    Cater, React, Trace, Earth, Heart, Quids, and Squid, assuming that they’re all correct, are what you need to find the rest of the words.

    I think the method would be to go through the list and see the letters common in each word to the ones you already know. the more you discover, the easier it becomes.

    ill try to get a complete list up soon.

  7. 7. Locke Said:

    Well, i found a few. Acorn, Dimer, Fades, Glyph, and Icons all fit the pattern. all together thats 12. almost halfway done.

  8. 8. Locke Said:

    Revised List.
    My previous list made a few letters impossible, i think.
    Anyways, here’s what i got down to N.
    Acorn, Brawn, Cater, Drive, Earth, First, Glyph, Heart, Irons, Joked, Klutz, Lumpy, Mache(as in Paper Mache, not to sure about this one.), and Nacho. Also there is Squid, Quids, React and Trace, as was mentioned before.

  9. 9. Locke Said:

    I’ve a sneaking suspicion that this isn’t the only possible solution, but here’s my complete list.

    Acorn, Brawn, Cater, Drive, Earth, First, Glyph, Heart, Irons, Joked, Klutz, Lumpy, Mache, Nacho, Olive, Pique, Quids, React, Squid, Trace, Umbra, Vixen, White, Xylem, Yacht, Zilch.

    Someone check me, but i believe i’m correct.

    My method of solving this was to type in “5 letter words that start with _” in google, and once i found an acceptable list, check the words on the list to both the chart and the words i already had. Time consuming, but effective.

  10. 10. Random Guy Said:

    Continuing with where Wizard of Oz left of, we can check whether the words as said above are correct by comparing them against each other, ie. C and Q.
    Lets start with C-(other letters)

    C-E=4
    Cater and Earth have 4 common letters, so we can assume they are correct.

    C-Q=0
    Cater and Quids have no common letters, so we can also assume they are correct.

    We do not need to check for H and Q, as they have the same letters as E and Q respectively. Now we just need to check E/H and Q/S

    E-Q=0
    Earth and Quids have no common letters too, so we can also assume they are correct.

    Check complete. Words fit their descriptions. :D

  11. 11. Rp123 Said:

    ACORN
    BRAWN
    CRATE
    DRIVE
    EARTH
    FIRST
    GLYPH
    HEART
    IRONS
    JOKED
    KLUTZ
    LUMPY
    MACHE
    NACHO
    OLIVE
    PIQUE
    QUIDS
    REACT
    SQUID
    TRACE
    UMBRA
    VIXEN
    WHITE
    XYLEM
    YACHT
    ZILCH
    Is this the answer? I don’t know if it is right. I have a doubt on Umbra, because no other word called to me.

  12. 12. Wizard of Oz Said:

    So, where have we got to now?

    Let’s assume that we have the first seven words correct beginning with C, E, H, Q, R, S and T as above. What next?

    Let’s take the letter M. This has three letters in common with each of the words beginning with C, E, H, R and T, and none in common with those starting wih Q and S.

    Take the word CATER. The word beginning with M will have three letters from CATER plus one other letter not present in CATER or QUIDS. By my reckoning that gives ten possible combinations of three letters out of CATER, each one multiplied by the 15 possible letters not in CATER or QUIDS. That’s 150 unique combinations of letters. For each one of these 150 combinations there are 24 possible sequences of these letters to be tested for meaningful words. 3600 in all. And this is just for the letter M.

    I don’t think that my remaining years are long enough for me to work all this out. So maybe there’s a short cut through all of this that I can’t see right now.

  13. 13. Karl Sharman Said:

    I didn’t get as far as some! It appears Rp123 listed them first. Here is the published answer:

    (1) Use the 5’s as a break-in. That provides REACT, TRACE, CRATE, EARTH, HEART, SQUID, QUIDS. That’s a pretty good starting point. Then work out the P–with three overlaps with SQUID, the only word it can be is PIQUE. (Well, OK, I missed PIOUS. All for the best, though.)
    (2) Pick a letter with either a lot of 0’s, or a lot of overlap with words I have, or both.
    (3) Eliminate the letters with 0’s; mark all other letters as possible, but unmark letters in any known word with a 0 overlap
    (4) For known words with a non-zero overlap, note which letters are still possible for that word. Repeat as necessary. In this case: PIQUE has one letter of overlap, but I, Q, U, and E aren’t possible; the overlap must be P. Similarly, HEART has one overlap, which must be the H. (As does EARTH; having used that information in H, we can go ahead and eliminate that.)
    (5) With sufficient evidence, work out the word. In this case: the only word starting with G and containing a P, an H, and two of the letters KLMNOWXYZ is GLYPH.
    (6) Return to step 2. I worked out X next, figuring that not many words started with X and that I stood a good chance of knowing it; then Y, with its heavy overlap with both REACT and EARTH. Then L; then, roughly, U, B, I, F, J…the more known words, the easier it gets, of course.

    The complete list of words:
    ACORN
    BRAWN
    CRATE
    DRIVE
    EARTH
    FIRST
    GLYPH
    HEART
    IRONS
    JOKED
    KLUTZ
    LUMPY
    MACHE
    NACHO
    OLIVE
    PIQUE
    QUIDS
    REACT
    SQUID
    TRACE
    UMBRA
    VIXEN
    WHITE
    XYLEM
    YACHT
    ZILCH

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