There are 5 Humanoid Robots in a Space shuttle. Humanoid robots have hierarchy R1, R2, R3, R4 and R5.
R1 designation is the highest and R5 is the lowest.
These Robots have three characteristics :
a. Every robot is so greedy that it can even take lives of other robot to make more money.
b. Every robot desperately wants to stay alive.
c. They are all very intelligent.
There are total 100 gold coins on the ship. The robot with the highest designation on the shuttle is expected to make the distribution. If the majority on the shuttle does not agree to the distribution proposed, the highest designated robot will be thrown out of the shuttle(or simply plugged off). The first priority of the robot is to stay alive and second to maximize the gold they get.
Robot 5 devises a plan which he knows will be accepted for sure and will maximize his gold. What is his plan?
Solution :
The solution of this problem lies in thinking through what will happen if all the pirates were thrown one by one and then thinking in reverse order.
Let us name pirates as R1,R2,R3,R4,R5 hierarchy (R1 being highest).
If only R4 and R5 are left at end, R4 will simply give 0 coins to R5 and still escape because majority cannot be reached. Hence, even if R5 gets 1 coin he will give his vote to the distributor.
If R3, R4 and R5 are there on the deck, R3 will simply give one coin to R5 to get his vote. And R4 simply gets nothing. Hence, even if R4 gets 1 coin he will give his vote to the distributor.
If R2,R3,R4 and R5 are there on the deck, R2 will simply give one coin to R4 to get his vote. R3 & R5 simply gets nothing.
If R1,R2,R3,R4 and R5 are there on the deck, R1 simply gives 1 coin each to R3 and R5 to get their votes.
Hence, in the final solution R1 gets 98 coins and only R3 & R5 get 1 coin each.
Let us name pirates as R1,R2,R3,R4,R5 hierarchy (R1 being highest).
If only R4 and R5 are left at end, R4 will simply give 0 coins to R5 and still escape because majority cannot be reached. Hence, even if R5 gets 1 coin he will give his vote to the distributor.
If R3, R4 and R5 are there on the deck, R3 will simply give one coin to R5 to get his vote. And R4 simply gets nothing. Hence, even if R4 gets 1 coin he will give his vote to the distributor.
If R2,R3,R4 and R5 are there on the deck, R2 will simply give one coin to R4 to get his vote. R3 & R5 simply gets nothing.
If R1,R2,R3,R4 and R5 are there on the deck, R1 simply gives 1 coin each to R3 and R5 to get their votes.
Hence, in the final solution R1 gets 98 coins and only R3 & R5 get 1 coin each.
Post your answer if you can other solution..
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#mechatronics
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