Riddles!

**TheQwertiest** · 05-09-2013, 10:07 AM

they pay as one and ask the cashier to separate them by color

TheGoldenGriffin · 05-09-2013, 10:22 AM

Take a package, open it, give one sock to the other man and keep the other. Repeat for all the others.

awpertunity · (This post was last modified: 05-09-2013 03:49 PM by awpertunity.)

40 people are captured and randomly have their face painted either red or blue. They are able to see the faces of all the others but not their own. They are ordered to line up one by one and guess the color of paint on their face. If they guess correctly, they are free to go, and if they guess incorrectly they are executed. They do not get to see after a person has guessed whether that person has been let go or executed. Before doing so, they are allowed to devise a strategy together but they are not allowed to have others tell them the color of paint on their face.

What is the best strategy and how many of them can be saved? (See below post for more details)

TheGoldenGriffin · 05-09-2013, 11:39 AM

Look at your own nose

bngn3000 · 05-09-2013, 11:41 AM

(05-09-2013 11:31 AM)awpertunity Wrote: 40 people are captured and randomly have their face painted either red or blue. They are able to see the faces of all the others but not their own. They are ordered to line up one by one and guess the color of paint on their face. If they guess correctly, they are free to go, and if they guess incorrectly they are executed. They do not get to see after a person has guessed whether that person has been let go or executed. Before doing so, they are allowed to devise a strategy together but they are not allowed to have others tell them the color of paint on their face.

What is the best strategy and how many of them can be saved?

39 can be saved. One person can blindfold everyone and separate them into two groups (one red and one blue). Since everyone is blindfolded and no explanation is given for the sorting, they are not being told which color they are. Once they remove the blindfolds they can deduce their color on their own. The sorter cannot be placed into a group because he understands beforehand what being sorted means.

**TheQwertiest** · 05-09-2013, 12:22 PM

they form a circle and each person tells how many are painted red and blue. everyone will be saved

awpertunity · (This post was last modified: 05-09-2013 01:13 PM by awpertunity.)

Okay sorry let me clarify a bit more:

While they are devising a strategy they are all blindfolded so nobody can see anybody's color Tongue

Then they will be put randomly into the line. Each person will then only be able to see the remaining people's faces before making a guess. And keep in mind the remaining people do not get to see the verdict of the person guessing (they do get to hear the guess though).

bngn3000 · 05-09-2013, 02:23 PM

The first person will guess the color of the second person and the second person will guess whatever the first person said. This way all even numbered people in line are guaranteed to survive and the odd numbered people have a 50-50 chance.

joelduque · (This post was last modified: 05-09-2013 03:27 PM by joelduque.)

All of them can be saved. A person assumes leadership. The leader would start pushing people around, grouping like colored people together. All would be sorted except himself. Then seeing this pattern, the rest should deduce the color of the paint on their face. The group with the same color as the leader's face would signal to him to come closer then he should also deduce the color of his face. Smile

Simpler solution with blindfolding during planning:

Blindfolded period: All agree to group into 2 groups with the same color on their face.

Leeway, not blindfolded, period: Execution of the above plan. Eventually they would sort into 2 distinct groups with either red or blue faces. At this point they should deduce the color of their face paint.

Randomization of the line and moment of truth: Each person correctly states the color of his own face.

awpertunity · 05-09-2013, 03:46 PM

(05-09-2013 03:11 PM)joelduque Wrote: All of them can be saved. A person assumes leadership. The leader would start pushing people around, grouping like colored people together. All would be sorted except himself. Then seeing this pattern, the rest should deduce the color of the paint on their face. The group with the same color as the leader's face would signal to him to come closer then he should also deduce the color of his face.
Simpler solution with blindfolding during planning:

Blindfolded period: All agree to group into 2 groups with the same color on their face.

Leeway, not blindfolded, period: Execution of the above plan. Eventually they would sort into 2 distinct groups with either red or blue faces. At this point they should deduce the color of their face paint.

Randomization of the line and moment of truth: Each person correctly states the color of his own face.

There is no leeway period lol.

Let me rephrase the whole problem to rule out any of the confusion:

- 40 people are captured and told each of their faces will be painted either red or blue

- If they can guess the correct color of their face, they live. Otherwise, they die

- The 40 people are allowed to deliberate on a strategy together BEFORE anyone's faces have been painted

- The 40 people are then no longer allowed to speak as their faces are painted and randomly put into a line.

- The first person to guess gets to see the colors of the 39 others' faces in the line

- The second person gets to hear the first person's guess but does not know the verdict and can only see the remaining 38 peoples' faces

Hope that's more clear! So far bngn3000's strategy is the only valid one and can guarantee to save 20 people and 50% chance for the remaining 20 people. Now who can do better? Tongue