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Product Value Puzzles

Assign each letter of the alphabet a value as follows: A = 1, B = 2, C = 3, and so on. The product value of a word is the product of its letters. For instance, the word CAT has a product value of 60 because C = 3, A = 1, T = 20, and 3 × 1 × 20 = 60.

Puzzle 1: Find an English word with a product value of 3,000,000.

(This puzzle has been attributed to Princeton mathematician John Horton Conway. Rumor has it that NPR puzzlemaster Will Shortz stated this puzzle on the air many years ago and attributed it to J.H.C. When we at first heard the puzzle, it was also stated that there was a unique English word with a product value of 3,000,000. As it turns out, that's not true. There are two such words.)

Puzzle 2: How many four-letter English words have a product value greater than 100,000?

(If you need some help, check out this list of all four-letter English words contained in the Official Scrabble Players Dictionary, 4th edition. Please note that some of these words may not be appropriate for all audiences. Viewer discretion is advised.)

Related Resources

You can use the Product Value Calculator to find all words with a given product value. (Except, of course, those words with a product value of 3,000,000. Those words you'll have to find on your own.)

On that page, you can also automatically calculate the product value for any word you enter. Of course, you could do that yourself with a basic calculator.