Three Shirts

Logic Level 1

Mr. Red, Mr. Blue, and Mr. Green are sitting at a table.
One man is wearing a red shirt, the second a blue shirt, and the third a green shirt.

Mr. Blue says, "Have you guys noticed how we're all wearing shirts of different colors from our names?"

The man in the green shirt replies, "Yes, Mr. Blue, I just noticed that!"

What is the color of the shirt that Mr. Blue is wearing?

Red Blue Green

4 solutions

Toshit Jain
Mar 6, 2017

Mr. Blue , as said earlier , is not wearing blue as it is same as his name. Mr. Blue is left with red and green shirts. He can't wear green as the other person is wearing green. So, Mr. Blue is wearing a RED shirt!

Moderator note:

The diagram below shows the situation given that none of the men are wearing a shirt that matches their name.

Then it's established Mr. Blue can't be wearing a green shirt.

This forces Mr. Red to be wearing green (as Mr. Blue and Mr. Green aren't options for the green shirt) and Mr. Blue to be wearing red (since he can't wear blue or green).

Then Mr. Green must have the only choice remaining, blue.

Going back to the situation where none of the men are wearing a shirt that matches their name, note that any statement of the format "Mr. X can't be wearing a Y shirt" (where X and Y are different colors) will force a specific solution to the puzzle. Do you see why?

Yes , because we have only three colour options. They are not wearing a shirt that matches their name . This leaves us with two colours only . If , anyhow , we are made familiar with one more colour (as in case you said above) , then we will be left with a single colour only which will force a specific solution to the problem . I hope I am clear . Thanks for the solution above.

Toshit Jain - 4 years, 2 months ago

Yea, both your solution and the challenge master's solution are correct.

However, the challenge master's solution will become more useful/easier if the number of variables (or in this case, the number of people involved increases). Like say, red/green/yellow/orange/blue/etc...

Pi Han Goh - 4 years, 2 months ago

@Pi Han Goh Agreed! ✌

Toshit Jain - 4 years, 2 months ago

Saanika Gupta
Mar 12, 2017

Huge Hint: the man in the GREEN SHIRT responds to Mr. Blue Therefore Mr.Blue is wearing red as he cant be wearing blue and another man is already wearing green

Yes, that is the tricky bit of hint one has to look for.

What if we were trying to solve this puzzle for four people? How many such hints would we require?

Agnishom Chattopadhyay - 4 years, 3 months ago

Very interesting puzzle! Simple but require very sharp processing of the given information. Before start processing the conversation among the men, we have to lay out all the possibilities; Since all of them wearing different color then their name, for example, Mr. Red can only wear either blue or Green color shirt. We can show all the possibilities as below:

Mr. Red {Blue, or Green}; Mr. Blue {Green, or Red}; Mr. Green {Red, or Blue};

Now notice that Mr. Blue start the conversation (who is either wearing Green or Red shirt) and the reply has come from the man wearing Green shirt, that imply Mr. Blue is not wearing Green shirt. So there is only one possibility; Mr. Blue is wearing Red shirt.

Mahabubul Islam - 4 years, 3 months ago

I agree, in such problems it is important to list all the possible cases (possibly in a tabular form), and then analyze the consequence of each piece of given information to see which cases can be eliminated.

Pranshu Gaba - 4 years, 2 months ago

Can they see their own shirt?

Richard Boyd - 4 years, 3 months ago

That doesn't matter whether they can see their own shirt or not

Mahabubul Islam - 4 years, 3 months ago

I don't understand. Does it matter? Is this an important issue to be addressed?

Pi Han Goh - 4 years, 2 months ago

var mB; mR; mG; sB; sR; sG find mB sachant que != sB mB = sR ou sG

     mR - mB - mG

mB say = "wearing != shirt" sG say = "y"

mB = sR

Fossemanant Fossemanant - 2 years, 8 months ago

Andrew Bishop
Mar 19, 2017

Let's break this down and see what each sentence tells us about Mr. Blue:

Mr. Blue says, "Have you guys noticed how we're all wearing shirts of different colors from our names?"

Their shirt colors do not match their names,therefore Mr. Blue is not wearing a blue shirt.

The man in the green shirt replies, "Yes, Mr. Blue, I just noticed that!"

The man in green is speaking, therefore Mr. Blue is not wearing a green shirt. The blue and green shirts have been eliminated, so the only remaining solution is that Mr. Blue is wearing a red shirt.

If the man speaking was wearing a blue shirt, can we still find the solution?

Christopher Boo - 4 years, 2 months ago

No, we could not. We already know Mr. Blue is not wearing blue, so if the man wearing blue replies, we won't learn anything new.

Andrew Bishop - 3 years, 11 months ago

Annie Li
Mar 18, 2017

Mr Blue is obviously not wearing Blue because that is his name and someone else is wearing green so therefore, he is wearing red

Yup, that's right! Can we also find the color of shirts that Mr. Red and Mr. Green are wearing?

Pranshu Gaba - 4 years, 2 months ago

Yes because Mr Blue is wearing red so therefore mr. red must be wearing green and Mr. Green should be wearing Red

Annie Li - 4 years, 2 months ago

This problem assumes that Mr. Blue is telling the truth when he says, "Have you guys noticed how we're all wearing shirts of different colors from our names?" It is not always the case in logic puzzles that all of the actors involved are telling the truth.

george palen - 3 years, 1 month ago

Not the point bro

Annie Li - 3 years, 1 month ago

Three Shirts

4 solutions

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