# The “guess what number I’m thinking of” problem

This post is, to some extent, a follow-up to my post on the two envelopes problem. As before, you're the subject of an experiment. Your adversaries, who I'll call "Team E", present you with two envelopes, each containing a slip of paper with a different number written on it. The numbers could be any (Real) … Continue reading The “guess what number I’m thinking of” problem

# The Two Envelopes problem

You are the subject of an experiment. You are presented with two closed envelopes, prepared by a group of people I'll call Team E. One of the envelopes contains twice as much money as the other, but you don't know the actual dollar amounts. You must choose one envelope (at random -- there's no other … Continue reading The Two Envelopes problem

# How long does it take to fall through a ball of ice?

Planet FrictionlessIceball has a straight, narrow tunnel connecting two points on its surface. How long does it take to slide through the tunnel? Simplifying assumptions As with most story problems, we have to make some simplifying assumptions. But I think they're fairly reasonable. We assume the faller starts out motionless, at one end of the … Continue reading How long does it take to fall through a ball of ice?

# A puzzle about a Fibonacci-like sequence

I'm thinking of a mathematical sequence, \$latex S\$, whose terms are all nonnegative real numbers. It is infinite in both directions. Like the Fibonacci sequence, it satisfies the relation: \$latex \displaystyle S_n=S_{n-1}+S_{n-2}\$ And we are given: \$latex \displaystyle S_0=1\$ What is the value of \$latex S_1\$? Surprisingly, you have enough information to figure it out. Note … Continue reading A puzzle about a Fibonacci-like sequence

# Superstalemate solution

This is a solution to the chess challenge I posed in a previous post. It is not the only solution. From this position: 8/7p/6p1/2K3pk/6pb/6p1/6P1/8 b - - 0 1 Black plays ...h6. Any move by white then stalemates black. Occasionally in a chess discussion group, someone will suggest that stalemate being a draw is a … Continue reading Superstalemate solution