Puzzles

Published on February 15th, 2013 | by Simi

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Puzzle Challenge 1

Roll up students – these puzzles are just for you!  Upload your answers to all four puzzles for a chance to win a signed Keith Devlin book. Correct submissions will be ordered and numbered by submission date. The winner will be selected at random using the excel random number function. Submissions close March 31st

Puzzle courtesy of Brian Davey, Department of Mathematics and Statistics, La Trobe University.  Puzzles are given weekly to first-year Mathematics and Statistics students at La Trobe.

#1: BERYL’S QUILT

Beryl has made the incomplete quilt of 8 squares shown above, and she doesn’t have any material left for the missing square.

Can Beryl make a square quilt using all the material shown, by making only two straight cuts?

Beryl may not fold the material before making a cut, nor may she cut two separate pieces of material with one cut.

 

#2: EGG TIMER

You are given two egg timers that measure
3 minutes and 5 minutes, respectively.

• Using these two egg timers, you want to take a shower that lasts exactly 4 minutes.

How can this be done?

• What is the least amount of time required to take your 4-minute shower, measured from the moment you start one of the timers?
• Show that it is possible, using these two egg timers, to take an n-minute shower, for all n ϵ N.
• For each n ϵ N, what is the least amount of time required to take an n-minute shower, measured from the moment you start one of the timers?


#3: THE SWENSENS’ BLOCK OF LAND

The four Swensen brothers have bought a block of land, consisting of 36 squares, with four trees and four ponds as shown on the plan below.

They’ve asked Caitlin the architect to divide the block of land, using the grid lines shown, into four identically shaped plots. The problem is that each brother would like one tree and one pond on his individual plot.

Can she do it? How?

Map of block of land

#4 HANDSHAKES

My partner and I went to a dinner party last weekend, at which there were four other couples.

At the start of the party, some handshaking took place. Of course, no one shook hands with themselves. Also, no one shook hands with their own partner, and no one shook hands with the same person more than once.

Just before the dinner started, I asked everyone else at the party (including my partner) how many people they had shaken hands with. To my surprise, everyone gave a different answer.

How many people did my partner shake hands with?

 

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