Three blue and two red hats puzzle
At a party, four people played a game. Three of them sat one behind the other, so that Abe saw Bill and Cal, and Bill only saw Cal, who sat in front and saw nobody else.
Dave had 5 hats which he showed to his three friends. Three of the hats were blue and two were red.
Now Dave placed a hat on the head of each of his three friends, putting aside the remaining two hats.
Then he asked Abe what color his hat was.
Abe said he couldn’t tell.
Bill was asked the color of his own hat, but he didn’t know for certain either.
Cal, though he couldn’t see any hat at all, gave the right answer when asked what color his hat was.
Do you know what color Cal’s hat was and how he reasoned to find out the correct answer?
Color of Cal’s hat?
Abe doesn’t know which hat he is wearing, so the two in front must be either 1 red 1 blue or 2 blue. Can’t be 2 red or Abe would know his is blue.
Bill doesn’t know which hat he’s wearing, but he knows it must be 1 red 1 blue or 2 blue. If the hat in front is blue, then he would know his is red. Therefore the hat in front must be red.
Cal’s hat is red.
This is not correct.
Abe sees at least one blue hat.
If Bill sees a red hat he knows he must have a blue hat.
But Bill doesn’t know what hat he haves so he must be seeing a blue hat.
So Cal’s hat must be blue.
Yup, I inverted the logic at the end by accident – good spot.
To correct mine:
Bill doesn’t know which hat he’s wearing, but he knows it must be 1 red 1 blue or 2 blue. If the hat in front is red, then he would know his is blue. Therefore the hat in front must be blue, and Cal’s hat is red.
Cal’s hat is blue.
If Abe sees two red hats he would know his hat is blue.
So he sees at least one blue hat. The other one can either be red or blue.
If Bill sees a red hat he knows he must have a blue hat.
But Bill doesn’t know what hat he haves so he must be seeing a blue hat.
“So he sees at least one blue hat”
There are 3 blue hats, so all 3 can be blue. This isn’t a guarantee that one of the front 2 is blue.
Your Answer
More puzzles to try-
Which day was the day before yesterday
The day after tomorrow is the third day after Wednesday. Which day was the day before yesterday?Read More »Whats the next number in the below number sequence pattern.
Whats the next number in the below number sequence pattern.Read More »Where can this marriage can be done legally
If a man wants to marry his widow’s sister legally, which country should he choose to do it legally?Read More »Who are the killers?
A very famous chemist was found murdered in his kitchen today. The police have narrowed it down to six suspects. ...Read More »Balls in Bag
A bag contains 64 balls of eight different colours. There are eight of each colour (including red). What is the ...Read More »Dorry The Dragon and the Ball
Dorry the Dragon just can’t help himself….he loves beach balls! Unfortunately, beach balls don’t like him much – they tend to ...Read More »Find the different paths possible
Consider a rectangular grid of 4×3 with lower left corner named as A and upper right corner named B. Suppose that starting ...Read More »What has many teeth, but cannot bite?
What has many teeth, but cannot bite?Read More »Find the wrong in Picture
What is wrong in the below Picture?Read More »Maths Aptitude Puzzle
Find the next number in the series 12, 20, 40, 72, 116, 172 ?Read More »Name The Car Parts
The list of words below all relate to the topic of ‘car parts’. The code used for each word is ...Read More »Half Filled barrel
We have shown you a regular water barrel as below. Without using any measuring device can you check if the ...Read More »GPS and 8 Battery Puzzle
You have a GPS that takes 2 working batteries. You have 8 batteries but only 4 of them work. What ...Read More »Lion, Goat and Grass Puzzle
A Man wants to bring a Lion, a goat, and Grass across the river. The boat is tiny and can ...Read More »What was John buying riddle
John walked into a hardware store and asked the price of some items. The salesman said: One costs $1, Eight ...Read More »Keyboard Words
Keyboard words are not in alphabetical order, Why?Read More »What is the probability that it was a penny?
Mary had a coin purse with fifty coins, totaling exactly $1.00. Unfortunately, while counting her change, she dropped one coin. ...Read More »Game of Cards
13 decks of cards have been mixed. What is the minimum number of cards that must be taken out from ...Read More »Akbar and Birbal dream puzzle
Akbar and Birbal are strolling in a garden. Akbar says,”You know Birbal, I had a dream last night,in which both ...Read More »2nd smallest number puzzle
There is 38 numbers. What is the least number of comparison needed to find the 2nd smallest out of them?Read More »