8

If the first player is the one who says either 2nd January or 1st February, then the winning player is Proof: The first player The strategy is to Note: I assumed that the game only goes over one year. If players can go on to the next January, then


7

Best solution my computer could find: 7---6 /| /| 4---2 | | | | | | 1-|-3 |/ |/ 5---8 Note that the property that all errors are up to sign the same follows easily With this solution portions are sized so you


6

Your second interpretation is the correct one, but your picture of the steps that Mike visits is incorrect. Diego visits steps Mike visits steps: Note that Mike visits Therefore the answer is:


5

Because the total score for all three contestants over three events The highest possible $b$ is Since Marina placed second in rhythmic gymnastics, With these values, there is only one way to get Sakura and Hina's scores of 10 and 9 respectively;


4

The key here is to draw pictures. Let's say we have the two initial hunters, with their bread pieces represented as numbers: o o (5) (3) Then the third hunter appears: o o o (5) (3) (0) In order to "share all their breads equally", they will need to distribute the bread so that each person has an equal amount of bread. Therefore, since the ...


4

One key observation is that So if there are more Fridays and Saturdays than other days of the week in the year Marina was born then it must be that Finally Now you are not asked for her birth year but given that she is between 20-29 years old in 2012 we find that


3

Actually, this can be solved even without using information about "Fridays and Saturdays".


1

First of all, how do we find the winning probabilities given the agents' numbers of bullets and chambers? This is pretty straightforward if there are only two agents. In this case, whoever first fires an actual bullet will win. Suppose they have probabilities $p,q$ of doing so on a given turn (so these are the ratios bullets/chambers for the two agents) and ...


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