Two players alternatively erase some 9 numbers from the sequence 1,2,...,101
until only two remain. The player that starts wins x−54 dollars from the
player that plays second, x being the absolute value of the difference between the remaining
two numbers.

Would you rather be the first or the second player?

Explain your decision by providing your strategy.

Continuing on

the pills problem.

Mowing a lawn 5 acres in size is part of a community service project. A group of people, including boys, girls, ladies and men, take up the job. They continue until the job is done. The grass also is growing at a constant rate hence the job increases if the number of days are higher but on the opening day job is the same.

a) 6 boys and 3 ladies can do the job in 4 days.

b) 8 girls & 3 men can do it in 3 days, which is the same as the time taken by 3 men and 6 Ladies.

c) Men work twice as fast as boys.

d) If only a girl were to do the job she would never be able to complete the job.

One day they reach the place of work and find that there are four bowls containing pills ( Either Poison pill or Energy pill ) kept for each category. (Marked- Boys, Girls, Ladies & Men). After consuming a poison pill their rate reduces to one third and after consuming an energy pill their rate becomes double. Three of these bowls contain one type of pill & one contains the other type.

In all, eight persons are present and there is at least one member from each category. They each take one pill from their respective bowl and start working. The job was completed in 9 days and the number of ladies is not more than the number of boys. How many boys, girls, ladies and men were present and which pill did they have?