Triangles
How many triangles can you find in this figure?
The Old ‘Rope around the Equator” Puzzle
You tie a rope tightly around the Earth’s equator then add three feet to its length and raise it evenly as high as possible. Can a cat now get under the rope?
Timepieces
A sundial has no moving parts. What timepiece has the most moving parts?
Reservoir
A reservoir is nearly empty but doubles the amount of water it holds every day until it’s full on the 30th day. What day did it become half full?
Kids
“My daughters are all blond, except two. They are also all redheads, except two. And they’re all dark-haired, except two. How many daughters do I have?”
Sequence
What’s the next letter: D R M F S …
Water and Wine
You have two identical glasses. One contains 8 ounces of wine, the other 8 ounces of water. Pour exactly one ounce of water into the wine, stir thoroughly and pour 1 ounce of the mixture back into the water. Is there now more water in the wine or wine in the water?
Boy-Girl
Legendary puzzler/mathematician Martin Gardner posed this one decades ago — and it’s still being argued over! Ms. White has two children, at least one of which is a boy. What’s the probability that the other child is a boy?
Yellow
What’s the area of the yellow rectangle?
Barry Evans (he/him, barryevans9@yahoo.com) wants you to know that The New Humbook is in most local bookstores and gift shops.
Answers to
Midsummer Puzzle Time
Triangles: 24
The Old ‘Rope around the Equator” puzzle: Yes, there’s a 6 inch clearance.
Radius R = Circumference C/2π
Adding one foot to C: R’ = C’+1/2π
Difference in radii R’ – R = 1/2π = 0.16 yards or about 6 inches. (The result is independent of the length of the rope.)
Timepieces: An hourglass (thousands of grains of sand).
Reservoir: 29 days (On the 30th day, it goes from half-full to full.)
Kids: Three, one of each.
Sequence: L (Do, Re, Mi, Fa, Sol, La …)
Water and Wine: The amount of wine in the water glass equals the amount of water in the wine glass, since each is replacing the other. (The numbers are irrelevant.)
Boy-Girl: Either one in two or one in three, depending on how you obtained the information.
1. You meet Ms. White in the park, who is with her son. She tells you, “I have one other child at home.” This other child is either a boy or girl, so the probability is one in two.
2. You hear from a friend that Ms. White has two children, one of which is a boy. The ordered (i.e. eldest-to-youngest) possibilities for a two-child family are GG, GB, BG and BB. Eliminate GG (since at least one child is a boy), and one of the remaining three is BB, so the probability is one in three.
Yellow: 81
Let h = height of rectangle = radius of quarter-circle; r = radius of half-circle.
Draw radius (red) as shown.
9 and r are legs of a right-angle triangle with hypotenuse h + r. So 92 + r2 = (h+r)2
Expanding and canceling r2, 81 = h2 + 2xhxr = h(h + 2r) = area of rectangle.
This article appears in Miranda’s Rescue Under Scrutiny, Part 1.