Math Puzzle Wiki - User contributions [en]

Coin game

2013-03-16T20:50:26Z

Test3: Created page with "Here is game I heard on the math factor ==Puzzle== Suppose you have eight coins of various denominations. Line these coins up in a line. You and your opponent take turns t..."

Here is game I heard on the math factor

==Puzzle==

Suppose you have eight coins of various denominations. Line these coins up in a line. You and your opponent take turns taking a coin from either end of the remaining line. The goal of the game is it end up with more money that your opponent. Should you go first or second, and what is the winning strategy?

{{Hint| There is a winning (although not optimal) strategy which works because there are an even number of coins. The strategy would not work for an odd number of coins}}

[[Category:New]]
[[Category:Games]]
[[Category:Combinatorics]]

Cannibals and missionaries

2013-03-16T20:44:49Z

Test3:

A classic crossing puzzle. Good practice in keeping track of information and presenting a solution.

==Puzzle==

Deep in the heart of the Amazon, three missionaries traveling with three cannibals come to a river. The only way across is a small boat. The boat will only hold two people at a time, and must be rowed back and forth across the river. Complicating matters is the missionaries' firm belief that if ever they found themselves outnumbered by the cannibals on one side or the other (in the boat or on land), the cannibals would scarf them down. How can all six travelers safely cross to the other side of the river?

{{Needs answer}}

==Variations==

This time, only one of the missionaries and only one of the cannibals know how to row the boat. Does this make the problem harder or easier (or make no difference)?

==Mathematical Content==

One way to solve the problem is to consider every possible allowable combination of cannibals and missionaries on the near bank of the river. Let each be a vertex of a graph. Then connect any two vertices if it is possible to get from one to the other through a valid trip of the boat back and forth. Finding a solution to the problem is now as easy as finding a path through the graph.

==See also==

*[[Farmer and the boat]]
*[[Three couples]]

==References==

[http://www.learn4good.com/games/puzzle/boat.htm: Flash game] - This amusing web app lets you try out your solution. A huge help if you are stuck or have trouble keeping track of everyone.

{{Averbach}}

[[Category:Crossing puzzles]]
[[Category:Graph theory]]

Chests of logic 4

2013-03-16T20:44:02Z

Test3:

I made this one up for my discrete math students. I'm not sure if it is easy or not.

==Puzzle==

As you enter the chamber, your eyes immediately fall on the four chests. One is made of solid gold, another out of silver, the third out of brick and the last out of wood. Legend states that one of the four boxes contains a priceless treasure, however all the others are filled with angry scorpions (also known as ''scorpions''). Luckily, attached to each box is a sign. Unluckily, you do not know which signs are true. The signs read:

:Gold box: "If the treasure is in the brick box, then the sign on the wood box is false."
:Silver box: "The treasure is in either the brick box or the wood box."
:Brick box: "Only one of these four signs is true."
:Wood box: "The signs on the metal boxes are either both true or both false."

Which box should you open?

{{Needs answer}}
{{Needs solution}}

==See also==

*[[Chests of logic]]
*[[Chests of logic 3]]
*[[Detective Merlin]]

[[Category:Logic]]
[[Category:Liar puzzles]]
[[Category:Logic puzzles]]
[[Category:New]]

Gem thief

2013-03-16T20:37:41Z

Test3:

Here is a liar/truth-teller puzzle I made up for an exam.

==Puzzle==

Detective Ruby Gould is investigating the theft of some rare gemstones. She has ﬁve suspects (named Al, Bob, Chris, Dan and Eliot). Each suspect either always lies or always tells the truth. Using the statements below, ﬁnd the thief. Can you also determine which suspects are liars and which always tell the truth?
:Al: “Bob or Chris stole the gems.”
:Bob: “That’s false! It was either Chris or Dan.”
:Chris: “I agree, Al is a liar.”
:Dan: “Only one of us is truthful.”
:Eliot: “The thief always tells the truth.”

{{Needs answer}}
{{Needs solution}}

[[Category:Liar puzzles]]
[[Category:Logic]]

Blind unshuffle

2013-03-16T20:37:01Z

Test3:

Imagine you are in a pitch-black room with a standard deck of playing cards. You have been
told that 10 cards in the deck are face-up and the other 42 are face-down. In order to be released
from the room, you must reorganize the deck of cards into two piles (without being able to see!) so
that each pile contains an equal number of face-up cards. How will you do it?

{{Needs answer}}
{{Needs solution}}

[[Category:New]]
[[Category:Needs answer]]

Fat travelers

2013-03-16T20:36:06Z

Test3:

Another nice crossing puzzle, as seen at Maths is Fun.

== Puzzle ==

Four travelers (Al, Bob, Chris, and Zoe) come to a river and find an old boat, with a sign reading "Weight limit: 300 lbs!" Unfortunately, Al weighs 270 lbs, Bob weighs 230 lbs, Chris weighs 180 lbs and Zoe weighs 120 lbs (as she is only 10). They also have 50 lbs of supplies. How can the fat travelers cross the river without sinking the boat?

{{Needs answer}}
{{Needs solution}}

== References ==

{{Mathisfun}}

[[Category:Crossing puzzles]]
[[Category:Optimization puzzles]]

Quarter cover

2013-03-16T20:24:08Z

Test3: Created page with "Here is a puzzle from Peter Winkler I first heard on the Math Factor ==Puzzle== Suppose you have a rectangular table which is just large enough to hold 100 non-overlapping q..."

Here is a puzzle from Peter Winkler I first heard on the Math Factor

==Puzzle==

Suppose you have a rectangular table which is just large enough to hold 100 non-overlapping quarters (101 quarters will not fit). Of course, not all of the tabletop is covered by these quarters. Prove that you can cover the entire tabletop (with no gaps) using 400 quarters.

{{Needs hint}}
{{Needs solution}}

[[Category:New]]
[[Category:MCP]]
[[Category:Geometry]]
[[Category:Combinatorics]]

High school play

2013-03-16T20:17:53Z

Test3:

Here is an example of an easy to solve logic puzzle.

== Puzzle ==

Four friends (named Chris, Harry, Katie, and Sam) tried out for a 4 person play, and each got a part (the available parts were King, Queen, Peasant, and Tree). From the information below, determine which part each friend received.
<ul>
<li> The director thought it was important for the King to be played by a boy and the Queen to be played by a girl. </li>
<li> Chris was disappointed to not be playing royalty.</li>
<li> Katie was happy that her boyfriend Sam would not play the Peasant.</li>
<li> Harry's sister was cast as the Tree.</li>
</ul>

{{Hint| Make a table with rows for the people and columns for th parts. Check off combinations you know are correct, and mark those you know are impossible.}}
{{Needs answer}}
{{Needs solution}}
== Similar puzzles ==

[[Prom problem]]

[[Category: Logic puzzles]]