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Chapter 1
Playful Puzzles
1
Word Mystery
What word has 8 letters, sometimes has 9 — it always contains 8 letters, occasionally uses 12 though! Find either of two answers.
2
Salary Secrecy
A group of 5 employees is at lunch and the subject of their average salary comes up. They all want to know the average but don’t want to give information to any other about their own salary. Each has a pencil and piece of paper and there is no one else to assist them. How can they meet their objective?
3
Relations Puzzles
(a)A man points to another man and says: “Sons and daughters have I none but that man’s father is my father’s son.” How are the two men related?
(b)Ray’s son-in-law is my Uncle Bob’s father. If I am related by blood to Ray how is Ray related to me?
(c)“Daughters and nephews have I none but Chris’s father-in-law is my mother-in-law’s son.”
(i)What is the speaker’s gender?
(ii)What is Chris’s gender?
(iii)How are the speaker and Chris related?
4
Slider
Use only five sliding block moves to get the piece labeled T to the lower right corner. A move is one piece moved along any path.
5
Fastest Serve
A tennis player hits a serve that in kilometers per hour (kph) is exactly 100 more than when expressed in miles per hour (mph). How fast did he serve?
6
The Population Explosion
In March 2015 the estimated population of the earth reached 7.3 billion people. The average person is estimated to occupy a volume of 0.063 m3 so the volume of the total population is 0.4599 km3.
(a)Model the earth as a sphere with a radius of 6,371 km and spread the volume of people over the surface of the earth in a shell of constant thickness. How thick is the shell?
(b)The population currently grows geometrically at 1.14% a year. How long will it take at this rate for the population to fill a shell one meter thick covering the earth? What will the population be then?
(c)At the 1.14% geometric rate how long will it take and what will the population be to occupy a sphere with a radius expanding at the speed of light (= 9.4605284 × 1012 km/yr)? Ignore relativistic effects.
7
Catenary
A 15 meter chain hangs from two vertical 10 meter poles placed d meters apart. The low point of the chain hangs 2.5 meters from the ground. What is d?
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Chapter 2
Geometric Puzzles
8
Mining on Rigel IV
An amazing thing about the planet Rigel IV is that it is a perfectly smooth sphere of radius 4,000 miles. Like the earth it rotates about a north pole so a latitude and longitude system of coordinates referenced to the poles serves to locate positions on Rigel IV just as it does on earth. Three prospectors make the following reports to headquarters.
(a)Prospector A: “From my base camp I faced north and went 1 mile in that direction without turning. Then I went east for 1 mile. I rested for lunch before facing north again and going 1 mile in that direction without turning. Finally, I went west for 1 mile and arrived exactly at my base camp.” What are the possible locations for base camp A?
(b)Prospector B: “From my base camp I went 1 mile north; then I went 1 mile east. I next went 1 mile south and, finally, I went 1 mile west and arrived exactly at my base camp.” What are the possible locations for base camp B?
(c)Prospector C: “From my base camp I went 1 mile north; then I went 1 mile east. I next went 1 mile south and, finally, I went 1 mile west and arrived at the most distant point possible from my base camp under these conditions.” What are the possible locations for base camp C and how far from base camp C does the prospector end up?
9
Linking Points
A straight line connecting any two points of the six points in the figure is a link. How many links can be placed without forming a triangle with three of the points as vertices?
10
Right Triangles
In the figure AE = 111 and other lengths are unknown. What is the value of AB2 + BC2 + CD2 + DE2?
11
The Clipped Polyhedron
A polyhedron, P1, has a small tip of each of its vertices sliced off by a plane to produce polyhedron P2. P2 has F faces, V vertices and E edges.
(a)One of F, V or E equals 11. What are the two possibilities for P1?
(b)One of F, V or E equals 13. What are the four possibilities for P1?
12
The Papered Boxes
(a)Aksana states to her friend, Josh: “I have an ideal rectangular box with integer dimensions and no top. I have papered both inside and outside (ten surfaces) and notice that, amazingly, the area of paper in square units is the same as the volume of the box in cubic units. Furthermore, my box has the maximum volume for this situation.” Josh replies: “My box has th...
