Question 498699: If the alphabet is written in order and each letter is given a consecutive number, starting at one. What word can be spelled and when the numbers are multiplied equal 7560?
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Note that 7560 = 10*9*12*7 (other factorizations possible). Assuming the word has at least one vowel, we note that the vowels A = 1, E = 5, I = 9, O = 15, U = 21. If we assume that E occurs once (cannot occur more than once because only one factor of 5), we can write 7560 as 5*(2*7*9*12) --> E + BGIL, so we can make BILGE. Or, we can write 2*7*9*12 as 9*12*14, 7*12*18, or 7*9*24. This implies E+ILN, E+GLR, or E+GIX. Note that with any of these letter combinations, we can use any amount of A's, so we can make LINE, LIEN, ALIEN, ALINE, ANILE, ELAIN, LIANE (I'm a tournament Scrabble player...). For E+GLR we have ARGLE, GLARE, LAGER, LARGE, REGAL, and even ALEGAR/LAAGER/AGLARE. E+GIX doesn't make any fours or fives.
You can try this "casework" by assuming the word doesn't have an E and then assume it has an I, O, U, or only A's. There are tons of words out there you can make.
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