A and B are playing the game of bulls and cows. The rules of the game are as follows.

A selects a word with distinct letters and B has to find it. B is allowed a maximum of ten guesses. After every guess A tells B the number of Bulls and Cows in the word.

Bulls are letters which appear in the correct location, and cows are letters which appear, but not in their correct location

For example, if A selects a word BOLD while B guesses LOUD. Then A's reply would be 2 Bulls and 1 Cow.(O and D are in the correct place while L is not). Note that A only tells the number of Bulls and Cows. He does not tells which ones are cows and bulls.

A selected a six letter word. The game proceeded as follows:

1. FRIEND - 0 Bulls, 2 Cows
2. SQUARE - 0 Bulls, 2 Cows
3. GROUND - 0 Bulls, 3 Cows
4. FORMAT - 1 Bull, 0 Cows
5. TRAVEL - 1 Bull, 1 Cow
6. FORMAL - 0 Bulls, 0 Cows
7. FLIGHT - 2 Bulls, 0 Cows
8. SYMBOL - 0 Bulls, 1 Cow
9. FIGURE - 0 Bulls, 3 Cows


What is A's word?

(Assume that A's word is a valid English word and has 6 distinct letters.)

BUDGET

Because FORMAL had none, and FORMAT had a bull, the last letter must be the T.

In TRAVEL, the T is obviously the cow, and only the E or V could be the bull because RAL are all in FORMAL.  Statistically, the E is probably right at this point as it is the most commonly used letter in the English language, and words need vowels, in this case "distinct" vowels.

From here ... well, I lost my train of thought and don't feel like going through it again except to say, the next letter I figured out was the G as third to last, so I have ---GET.  Then I figured the U had to be one of the first two.  From there, it was easy to see BUDGET and those letters worked out fine.

-L

Posted by larry on 2005-03-02 01:32:33