The Hidden Beauty
It is rare when a word equation coincides with a number equation.
Share: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?
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.
29 March 2017, 3:55 pmDave:
“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)
29 March 2017, 8:36 pmtanyakh:
Great!
That was my point: TWELVE + ONE = TWO + ELEVEN in letters, as well as the corresponding numbers.
30 March 2017, 4:26 pmtanyakh:
I received a comment by pupugai that a similar equation exists in Russian. It includes numbers 5, 6, 15, 16.
30 March 2017, 4:27 pmAl Yunani:
In Greek also Tanya. 5=ΠΕΝΤΕ, 6=ΕΞΙ, 15=ΔΕΚΑΠΕΝΤΕ (10=ΔΕΚΑ), thus ΔΕΚΑΕΞΙ (pronounced “deka eksi” and meaning sixteen )=16.
1 April 2017, 6:59 amBut, since no anagram is involved…rather trivial I would say. 🙂
Αγγελος:
It does, but trivially so. 5 is пять, 15 is пятнадцать, 6 is шесть and 16 is шестнадцать.
1 April 2017, 7:00 amAl Yunani:
But, also the Russian seems pretty “trivial”. Right?
1 April 2017, 7:10 am5 = пять, 15 = пятнадцать, 6 = шесть and 16 = шестнадцать.
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.
4 April 2017, 1:44 pmTed R:
PS: And I suppose that NONE would be free?
4 April 2017, 2:47 pmTed 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).
4 April 2017, 4:39 pmtanyakh:
Ted R,
This is beautiful. (Your morning wasn’t wasted.)
5 April 2017, 3:45 pm≫ El problema verbal matemático más fácil del mundo. Rompecabezas dominical: Cuide sus decisiones:
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