Robano. 1 gave 1 gold coin to No.3, 2 to No.4 or No.5, and 97 to myself. The allocation scheme can be written as (97,0, 1, 2,0) or (97,0, 1, 0,2).
Push from the back to the front. If all the robbers from/kloc-0 to 3 feed sharks, only No.4 and No.5 are left, and No.5 will definitely vote against it and let No.4 feed sharks and take all the gold coins. Therefore, No.4 can only rely on supporting No.3 to save his life.
Knowing this, No.3 will put forward the distribution scheme of "100,0,0", and will leave all the gold coins to No.4 and No.5, because he knows that No.4 has got nothing, but he will still vote for it. With his own vote, his scheme will be passed.
However, if No.2 infers the plan of No.3, it will put forward the plan of "98,0, 1, 1", that is, give up No.3 and give No.4 and No.5 a gold coin each. Since the plan is more favorable to No.4 and No.5 than No.3, they support him and don't want him to be out and assigned by No.3 ... So No.2 took 98 gold coins.
Similarly, the scheme of No.2 will be understood by 1, and a scheme of (97,0, 1, 2,0) or (97,0, 1, 0,2) will be proposed, that is, No.2 will be abandoned and No.3 will be given a gold coin. At the same time, because of/kloc, This is undoubtedly the scheme that 1 can get the greatest benefit!
The second question:
10.
Because 210 =1024 >; 1000 is enough to indicate the status of these 1000 bottles (0- non-toxic, 1- toxic), which corresponds to the life and death status of mice (0- alive, 1- dead). For example, 000000000 1 01means that1and mouse No.3 are all dead, which means that the fifth bottle is poison.
1. For 1000 bottles, there are two states, toxic/non-toxic, represented by 1/0, so one bottle in 1000 is toxic (10000 .. 000), (.
2. Assuming that n mice do experiments, there are only two states of mice after one experiment, namely, life/death, then the mathematical model is used to solve the problem:
2^n & gt； 1000, obviously the smallest natural number n is 10. That is to say, the combination of life and death states of 10 mice can represent 1000 states.
Extending to solving the problem, you can feed ten mice like this. For the bottle of 1, the binary representation of 1 is 0000000 1, which means feeding it to the first mouse; For the second bottle, 2=00000000 10, that is, feed it to the second mouse; For the third bottle, 3=00000000 1 1, that is, feed it to the first and second mice; For the m-th bottle (m