Let P(x) be a polynomial with integer coefficients. Suppose that for three distinct integers a,b,c we have P(a)=P(b)=P(c)=-5, and that P(1)=6. What is the maximum possible value of a2+b2+c2?
Mac is idly tossing two dice when
he decides to see how many tosses it
would take to go from 1 to 6 in order.
The rules are to toss the two dice
until one or the other or both show
a 1. Then, toss until a 2 shows.
However, if both a 1 and a 2 show at the
same time, both can be used.
He then
tosses for a 3 and similarly for other
numbers. What is the expected number
of tosses to go from 1 to 6?
Four pegs begin on the plane at the corners of a square. At any time, you may cause one peg to jump over a second, placing the first on the opposite side of the second, but at the same distance as before. The jumped peg remains in place. Can you maneuver the pegs to the corners of a larger square?
Take the last name of a famous philosopher. Change the last letter to L. Rearrange the letters to get a type of meat. Who is it?
