perplexus.info :: Games : Bulls and Cows

Bulls and Cows (Posted on 2005-03-01)

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.)

Submitted by Sandeep

Rating: 4.5000 (8 votes)

Solution: (Hide)

BUDGET

First of all look at the 6th word, FORMAL. 0 Bulls and 0 Cows indicates that none of the letters are there in the answer. So our solution space has been reduced from 26 letters to 20 letters.
Next look at the 4th word, FORMAT. This gives T at last place.
Next look at the 9th word, FIGURE. F and R are already out. So we have three out of the four remaining letters (I,G,U,E).
Next compare the 1st word and 7th word. Suppose I is in the answer. Then, 1st says it is not at the third position while 7th says it is at the third position. A contradiction! Hence, I is not in the answer. So, we have G,U,E.
From the 7th word we get that G is at fourth position while from the 5th word we get that E is at the fifth position.

So far we have: ***GET
From 2nd word we get that U is not at third place. So it is either at the first place or at the second place. Porceeding on similar lines we can find the answer.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Solution	Math Man	2013-06-04 21:45:42
Answer	K Sengupta	2008-03-04 05:09:31
re(3): Solution	jenny	2005-03-12 03:08:14
re(2): Solution	Sachin	2005-03-12 03:01:39
re: Solution	jenny	2005-03-12 02:52:15
No Subject	Rex	2005-03-03 07:46:17
Solution	larry	2005-03-02 01:32:33
Solution verified.	john	2005-03-01 15:18:18
solution	Avin	2005-03-01 14:59:19
Solution	lauren	2005-03-01 14:47:12

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