The Hidden Beauty

It is rare when a word equation coincides with a number equation.

Problem. A store sells letter magnets. The same letters cost the same and different letters might not cost the same. The word ONE costs 1 dollar, the word TWO costs 2 dollars, and the word ELEVEN costs 11 dollars. What is the cost of TWELVE?

11 Comments

  1. James:

    Let x = cost of “O”.
    Let y = cost of “NE”.
    Let w = cost of “TW”.
    Let z = cost of “ELEV”.

    Then we have:
    x + y = 1
    w + x = 2
    y + z = 11

    From the first two equations, we have w – y = 1. Subbing for y, you get w – (11 – z) = 1 w + z = 12. Noting that w = “TW” and z = “ELEV” or “ELVE”, then w + z = “TWELVE”. So the cost of “TWELVE” is 12 dollars.

  2. Dave:

    “TWELVE ONE” is an anagram of “TWO ELEVEN” so the value of “TWELVE” is the sum of the values of “TWO” and “ELEVEN” less the value of “ONE” (or 2+11-1=12)

  3. tanyakh:

    Great!

    That was my point: TWELVE + ONE = TWO + ELEVEN in letters, as well as the corresponding numbers.

  4. tanyakh:

    I received a comment by pupugai that a similar equation exists in Russian. It includes numbers 5, 6, 15, 16.

  5. Al Yunani:

    In Greek also Tanya. 5=ΠΕΝΤΕ, 6=ΕΞΙ, 15=ΔΕΚΑΠΕΝΤΕ (10=ΔΕΚΑ), thus ΔΕΚΑΕΞΙ (pronounced “deka eksi” and meaning sixteen )=16.
    But, since no anagram is involved…rather trivial I would say. 🙂

  6. Αγγελος:

    It does, but trivially so. 5 is пять, 15 is пятнадцать, 6 is шесть and 16 is шестнадцать.

  7. Al Yunani:

    But, also the Russian seems pretty “trivial”. Right?
    5 = пять, 15 = пятнадцать, 6 = шесть and 16 = шестнадцать.

  8. Ted R:

    My gosh, when did Ls get so expensive? When I was a kid you could get 3 Ls and a pack of gum, all for a buck fifty.

  9. Ted R:

    PS: And I suppose that NONE would be free?

  10. Ted R:

    I guess my first joke backfired – it turns out that Ls are free! I had to dig around to find a few more equations, but if
    NONE = 0
    LOVE = 0 (a la tennis)
    ONE = 1
    LONE = 1
    TWO = 2
    TEN = 10
    ELEVEN = 11
    then (E, L, N, O, T, V, W) = ( 14/3, 0, -1, -8/3, 19/3, -2, -5/3 )

    Case closed (& morning wasted).

  11. tanyakh:

    Ted R,

    This is beautiful. (Your morning wasn’t wasted.)