Questions tagged [reachability]

A puzzle on a discrete system where one has to decide whether a certain system state can be reached through a finite number of steps.

Filter by
Sorted by
Tagged with
25
votes
1answer
2k views

Four is Cosmic!

This is a little puzzle I heard a while back from one of my mathematically inclined friends- I get the sense that it's bounced around a little, so forgive me if you've heard it. There is a sort of ...
72
votes
12answers
10k views

Turn off all lights in a ring-shaped palace

Not a very difficult question, but one I enjoyed nonetheless and wanted to share with the community. You are a servant in a palace. The palace is in the shape of a circle, and you do not know how ...
20
votes
2answers
1k views

Desegregate the Knights

You are given a 3 by 3 chessboard with a knight on each corner, where the knights in the top row are black and in the bottom row are white. On each turn, you may move a knight of either color (the ...
6
votes
2answers
2k views

Minimum moves to have all coins face Heads up

Given a circular list of coins, that all have Tails facing up. In each move, if we flip the coin at position $i$, then the coins at positions $i-1$ and $i+1$ get flipped as well. That is, consider: H ...
13
votes
2answers
2k views

The last number on the blackboard

The numbers $ 1, 2, \ldots, 500 $ are written on a blackboard. Each minute any two numbers are wiped out and their positive difference is written instead. At the end only one number remains. Which ...
12
votes
1answer
511 views

Enlarge the Square?

There are four stones, positioned on the ground at the vertices of a square. At any time, you may pick up a stone and "hop" it over another one so that it lands an equal distance beyond the hopped ...
13
votes
5answers
1k views

A row of 2015 red and white chips

There is a row of 2015 chips, of which 2014 are white and one is red. You are allowed to make moves of the following type: "Choose one red chip, and flip the colors of its two neighboring chips (from ...
12
votes
2answers
2k views

Averaging numbers on the blackboard

Aatif sees the numbers $ 1 , 2 , 3 , .... , 2016 $ written on the blackboard. In a move Aatif can pick any two numbers on the blackboard, erase them and write instead once their average. As an example,...
8
votes
2answers
611 views

Pathfinding with disappearing platforms - is it solvable?

This is a puzzle but might not have a solution. So "is it possible?" is a proper question. The puzzle idea was inspired by the question logic problem/puzzle solving, and if the puzzle here turns ...
11
votes
4answers
1k views

Another curious incident in the flea circus

The ringmaster of a flea circus puts four fleas $A$, $B$, $C$, $D$ on four different points in the plane that form the corners of a square. Whenever the ringmaster shouts "Hop!", one of the four ...
6
votes
2answers
5k views

Martin Gardner - Persistence

A number's persistence is : The number of steps required to reduce it to a single digit by multiplying all its digits to obtain a second number Then multiplying all the digits of that number ...
3
votes
4answers
196 views

A curious incident in the flea circus

The ringmaster of a flea circus puts three fleas $A$, $B$, $C$ on three different numbers on the real number line, so that flea $B$ sits exactly in the middle between $A$ and $C$. Whenever the ...
3
votes
2answers
222 views

A final incident in the flea circus: Part 1

The ringmaster of a flea circus draws a square $ABCD$ with corners $A=(+1,+1)$, $B=(+1,-1)$, $C=(-1,+1)$, $D=(-1,-1)$ in the Euclidean plane and picks a point $P$ with integer coordinates outside ...