Counting Liars Puzzle

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This is a puzzle from the Quantum Magazine that came by way of the Futility Closet.

“The population of the island of Pianosa is 100. Some of the inhabitants always lie; the others always tell the truth. Each islander worships one of three gods: the Sun god, the Moon god, or the Earth god. One day a visiting anthropologist asked each inhabitant the following questions:

  1. Do you worship the Sun god?
  2. Do you worship the Moon god?
  3. Do you worship the Earth god?

There were 60 “yes” answers to the first question, 40 “yes” answers to the second question, and 30 “yes” answers to the third. How many liars live on the island?”

Futility Closet added a link to a Truth/Liar puzzle send-off that was quite good:

Obligatory John Finnemore sketch:  “The guards and the Saphire City”  25 January 2012

Answer.

See Counting Liars Puzzle for a solution.

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Another Blank Clock

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This is a blank clock puzzle by Heinrich Hemme from Scientific American math puzzles.

“The hour, minute and second hands of this clock are all the same length and move smoothly in a circle. The dial contains hour and minute markers, but the numbers are missing. Therefore, it’s impossible to tell which one of the 12 hour markers belongs to the 12. The two hands on the left are positioned exactly on hour markers, and the hand on the right is positioned between a minute and an hour marker. What time does the clock show?”

Answer.

See Another Blank Clock for solutions.

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Zigzag Line Problem

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This is an interesting Talwalkar problem from 2021.

“Thanks to Lucas from Brazil for the suggestion! This problem is adapted from a Kangaroo Maths competition in 2020 for grades 9-10 (around 15 years old).

A circle has diameter AB. A line starts at A and zig-zags exactly 4 times between the diameter and the circumference until it ends at B, as shown.

If each of the angles the line makes with the diameter has the same measure α, what is α equal to?”

Answer.

See the Zigzag Line Problem for a solution.

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Knock the Bottle Problem

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This is a problem from Barry Leung’s Math Games.

“Larry and Julius are playing a game, taking turns throwing a ball at a bottle sitting on a ledge.  Larry throws first. The winner is the first person to knock the bottle off the ledge.  At each turn the probability that a player knocks the bottle off the ledge is ½, independently of what has happened before.  What is the probability that Larry wins the game?”

Answer.

See Knock the Bottle Problem for a solution.

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Clockwise Ant Puzzle

This is actually a travel problem masquerading as a clock puzzle from Futility Closet.

“A problem by Argentinian puzzlist Jaime Poniachik, from the February 1992 issue of Games magazine:

An ant crawls onto a clock face at the 6 mark just as the minute hand is passing 12. She begins crawling counterclockwise around the face’s circumference at a uniform speed. When the minute hand passes her, she reverses course and crawls clockwise without changing her speed. Forty-five minutes after her first encounter with the minute hand, it passes her a second time and she departs. How much time did she spend on the clock face?”

Answer.

See Clockwise Ant Puzzle for solutions.

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Ship and Seaplane Puzzle

This is a puzzle from Boris Kordemsky’s 1972 Moscow Puzzles.

“A diesel ship leaves on a long voyage. When it is 180 miles from shore, a seaplane, whose speed is ten times that of the ship, is sent to deliver mail. How far from shore does the seaplane catch up with the ship?”

Answer.

See Ship and Seaplane Puzzle for solutions.

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A Pair of Pretty Perimeter Puzzles

Here are two puzzles from Alex Bellos’s Monday puzzles.

“Ring it.  Each region has a perimeter given by its enclosed number. What is the length just along the edge of the entire figure?

Round the block.  Assuming all corners are right angles, what is the perimeter?

Today’s puzzles all come from … the Hyde Park Math Zine!  This delightful publication is written in pen on a single folded sheet of paper, has a print run of 30 copies, and is distributed in the neighbourhood of Hyde Park in Austin, Texas.

Fanzine culture is well established in sports and music. Math educator Kevin Gately thought the format would work for puzzles too. “It dawned on me that there might be people in my community who find the novelty of a hyper-local math zine to be amusing and/or curious,” he said. And it seems there are.

Each issue of HPMZ presents three problems, with easily understandable answers, and let’s not forget the cover artwork!  Gately’s puzzles are mostly taken from other sources, and tweaked. Here are [two] that took my fancy.”

Answer 1 ________  Answer 2

See A Pair of Pretty Perimeter Puzzles for solutions.

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