Can Do

A puzzle by Sam Loyd:

John the milkman has two 10-gallon cans full of milk. Two customers have a 5- and a 4-quart measure and want 2 quarts put into each measure. How can he accomplish this?

“It is a juggling trick pure and simple, devoid of trick or device, but it calls for much cleverness to get two exact quarts of milk into those measures employing no receptacles of any kind except the two measures and the two full cans.”

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An Observant Anthropologist

A puzzle from the 1998 Moscow Mathematical Olympiad, via Peter Winkler’s excellent Mathematical Puzzles, 2021:

An anthropologist is surrounded by a circle of natives. Each native either always lies or always tells the truth. The anthropologist asks each native whether the native to his right is a liar or a truth teller. From their answers, she’s able to deduce the fraction of the circle who are liars. What is the fraction?

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Two Weighings

A problem from the Leningrad Mathematical Olympiad: You have a set of 101 coins, and you know that it contains one counterfeit coin X. The 100 genuine coins all have the same weight, which is different from that of X. Using only two weighings in an equal-arm balance, how can you determine whether X is heavier or lighter than the genuine coins?

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A Late Mystery

In Lloyd C. Douglas’ 1929 novel Magnificent Obsession, a doctor dies of a heart attack, leaving behind a journal written in cipher. The first page is shown here. Can you read it?

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Where Did Nigel Go?

A puzzle from the excellent Riddler feature at FiveThirtyEight, via Oliver Roeder’s 2018 collection The Riddler:

Your eccentric friend Nigel flies from Heathrow to an airport somewhere in the 48 contiguous states, then hires a car and drives around the country, touching the Atlantic and Pacific Oceans and the Gulf of Mexico, then returns to the airport at which he started and flies home. If he crossed the Ohio River once, the Missouri River twice, the Mississippi River three times, and the Continental Divide four times, then there’s one state that we can say for certain that he visited on his trip. What is it?

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A puzzle from James F. Fixx’s More Games for the Superintelligent, 1976:

A man who likes trains walks occasionally to a nearby railroad track and waits for one to go by. Afterward he notes whether he saw a passenger train or a freight. After several years his notes show that 90 percent of the trains he’s seen have been passenger trains. One day he meets an official of the railroad and is surprised to learn that the passenger and freight trains on this line are precisely equal in number. If the man timed his trips to the track at random, why did he see such a disproportionate number of passenger trains?

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A brainteaser from the Soviet science magazine Kvant, via Quantum, January/February 1991:

Bobby found the sum of three consecutive integers, then of the next three consecutive integers, then multiplied these two sums together. Could the product have been 111,111,111?

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