Riddles!

[awpertunity]

(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.

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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?