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?

# Tag: puzzles

## 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

## The Balls and Urns Paradox

Start with an empty urn having an unlimited capacity, and a infinite number of balls, labeled “1”, “2”, “3”, etc. At time T minus 1 second, put balls #1-10 into the urn, then take ball #1 out. At time T minus 1/2 second, put balls #11-20 into the urn, then take ball #2 out. At…… Continue reading The Balls and Urns Paradox

## How to walk around the Earth

Suppose we start at Cape Horn, at the southern tip of South America. We are challenged to travel from there to Tasmania (the big island south of Australia). We can travel freely over land, but only for X consecutive kilometers over water. How small can X be, and still allow us to reach Tasmania? Ground…… Continue reading How to walk around the Earth

## 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

## Superstalemate: A chess challenge

Challenge: Find a legal chess position in which one player is stalemated, and in which the stalemated player would still not have any legal moves, even if the rules were changed to make it legal to move your king into check, or otherwise leave your king in check. I don’t think this is a very…… Continue reading Superstalemate: A chess challenge