Brain Teasers
Word on the Stone
The archaeologist Doug Wither-Trowel was excavating a site in France when he came upon a four-letter English word engraved on a stone. In his notebook, he wrote that no two letters were identical, if one replaced each letter in the word with a number giving its alphabetic position (A=1, B=2 etc) the total of the letters is 20, and the sum of any three of the numbers is exactly divisible by the fourth number. His French assistant, reading the entry in the notebook, claimed the word was French. What was the English word on the stone?
Answer
The English word was JADE (the French was DEJA). If the four numbers are W, X, Y and Z and their total is T then(W + X + Y)/Z = (T - Z)/Z
Since the left-hand side of the equation is a whole number then both (T/Z) - 1 and T/Z are also whole numbers. By symmetry, W, X, Y, Z are factors of T. The possible factors of 20 are 1, 2, 4, 5, 10, 20. The four of these that sum to 20 are 1, 4, 5, 10. Replacing these by letters gives A, D, J, E.
Hide Answer Show Answer
What Next?
View a Similar Brain Teaser...
If you become a registered user you can vote on this brain teaser, keep track of which ones you have seen, and even make your own.
Solve a Puzzle
Comments
Way too hard! No one is going to even attempt to solve this one!!!
very good job good exercise for the brain
Jul 12, 2002
Great one...did it in a couple of minutes, but didn't use the formula per se.
Loved it! Man, I can just feel my brain growing!
The largest number must be 10 - anything larger would not divide the sum of the others. There must be at least 1 vowel - A or E, or both ... then it falls into place.
A great teaser - thanks - was it original?
A great teaser - thanks - was it original?
To post a comment, please create an account and sign in.
Follow Braingle!