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Creative Thinking Puzzles III
Each puzzle has two hints which can be found at the back of the book.
48. Moving Clocks
Shown are seven clocks showing different times. Can you rearrange them among the seven positions, without changing their orientation, so that they all show the same time? [Solution 24]
49. Miserable Marriage
A woman’s husband was also stepfather to her children. Unfortunately, it was a loveless marriage and after describing him in her diary as shown she decided to separate. Can you remove one of the letters to assist her in leaving her husband? [Solution 58]
50. Out of This World
If you found an extra-terrestrial being like the one shown what would he be in? [Solution 46]
51. Doubtful Date
A man married his girlfriend on the date shown. If her minimum age had to be 18 how old was she? [Solution 35]
52. Door to Door
In Correspondence Close, exactly two of the three house numbers shown got to equal first place in a letter writing competition. What are the two numbers? [Solution 21]
53. No Earthly Connection
After his recent visit to Earth, Alpha the alien incorrectly drew the above. Nothing needs to be added to or removed from the drawing to correct it. Can you change the content of one of the small circles to rectify the picture? [Solution 55]
54. Water Puzzle
Mervin the magician has just turned water into wine. However, none of his audience at the Teetotal Club is particularly impressed. By relocating the cocktail stick and placing it horizontally, can you reverse the effect and change the wine into water? Can you also find a second solution by rearranging the stick vertically? [Solution 50]
55. Doing a Turn
Shown are three smokers performing a song on stage. The whole number is performed as a three-part harmony.
Q: What is it? [Solution 47]
56. The Tin Door
While exploring a cave, two adventurers unexpectedly found a locked tin door set into a wall. On the adjacent wall was a set of curious fractions. Can you decipher the message and discover what is in the secret room? [Solution 33]
57. Fish Feast
A shoal of fish were enjoying a swim when the fish at X decided to eat the five fish A–E. This it did by moving only along the straight lines, visiting each position once only and finally returning to X to swim along with the shoal. Now C was eaten some time before D who was not the last eaten, B was devoured some time before A and the route that was taken did not cross over itself at O. Can you draw the route that fish X took? [Solution 53]
58. Dig It
Shown is a stone, to the right of which is a spade stuck in the ground. Can you pick up the stone and add one straight line to the picture to show that the spade has sunk deeper into the ground? [Solution 60]
59. The Concealed Car
Behind one of the four glass doors is concealed a car. Door A has a letterbox and a push-bar, B shows an oval window, C exhibits a letterbox and a cat-flap, and D has a rectangular window and a push-bar. Which door is to be opened to reveal the car? [Solution 48]
60. Pet Theory
Can you add the four straight lines at the bottom of the picture to the shapes above them to complete the view of two identical pets? [Solution 37]
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Titan’s Triangle
There is a problem that often turns up in IQ tests that involves finding the number of shapes in a larger shape. An interesting example is shown below where the number of triangles of any size is to be counted in a triangle with side length four (n = 4).
Titan’s Triangle with n=4
A generalisation is provided here for a triangle of any size n, in which formulae are given for the total number of triangles, parallelograms, and trapezoids of any size. Initial results are also presented for the number of ways closed paths of length 4, 5, and 6 might be traversed, by focusing on specific shapes. The reader is invited to take up the project and make new discoveries of his own.
Number of shapes
If one wishes to find a formula for the sum of triangles Sn of any size in a triangle of side n, then care must be taken in applying a mathematical technique such as the calculus of finite differences because there are two cases, one for n even and the other n odd.
A calculation at n = 4 verifies that the answer to the problem given above is 27 (did you include the inverted triangle of size 2?). An arbitrary number of layers can be added to the triangle (the following figu...
