In a Word

ditation
n. enrichment

improficuous
adj. unprofitable

Another puzzle by Yakov Perelman:

“Two fathers gave their two sons some money. One gave his son 150 rubles and the other 100 rubles. When the two sons counted their finances, they found that together they had become richer by only 150 rubles. What is the explanation?”

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“The whole trick is that one of the fathers is the son of the other father. There are only three persons in this problem and not 4: grandfather, father and son. Grandfather gave his son 150 rubles and the latter passed on 100 of them to the grandson (i.e. his son), thus increasing his own capital by 50 rubles.” From Figures for Fun, 1957.

September 9, 2015September 20, 2015 | Language · Puzzles

Dizzy

Russian science writer Yakov Perelman asks: How many times must an 8-toothed cogwheel rotate on its axis to circle around a 24-toothed cogwheel?

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Four. “Generally speaking, when a body rotates round a circle, it always does one revolution more than one can count. It is precisely this that explains why the earth, revolving round the sun, succeeds in rotating on its axis not in 365 1/4 days, but in 366 1/4 days, if one counts its revolutions in respect to the stars and not the sun. You will understand now why sidereal days are shorter than solar days.” From Perelman’s Figures for Fun, 1957.

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August 30, 2015September 6, 2015 | Puzzles · Science & Math

Black and White

tanner chess problem

By John Tanner. White to mate in two moves.

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1. f4! Kxe4 2. Rc4# From E.B. Cook et al., American Chess-Nuts, 1868.

August 29, 2015September 6, 2015 | Puzzles

Nobody Home

pooh and piglet

A puzzle by S. Sefibekov:

Winnie-the-Pooh and Piglet set out to visit one another. They leave their houses at the same time and walk along the same road. But Piglet is absorbed in counting the birds overhead, and Winnie-the-Pooh is composing a new “hum,” so they pass one another without noticing. One minute after the meeting, Winnie-the-Pooh is at Piglet’s house, and 4 minutes after the meeting Piglet is at Winnie-the-Pooh’s. How long has each of them walked?

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Call Winnie-the-Pooh’s house W and Piglet’s house P, and call their meeting point M. Suppose it took x minutes for the two of them to travel from their starting points to M. Then Winnie-the-Pooh spent x minutes walking from W to M and 1 minute from M to P; hence WM/MP = x. And the same reasoning for Piglet gives PM/MW = x/4. Now, WM/MP x PM/MW = 1, so 1 = x²/4, and x = 2. Winnie-the-Pooh has walked for 3 minutes and Piglet for 6 minutes. From the Russian science magazine Kvant.

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August 25, 2015September 6, 2015 | Puzzles

Bright and Early

https://commons.wikimedia.org/wiki/File:2014_Meteor.jpg — Image: Wikimedia Commons

Meteors are more commonly seen between midnight and dawn than between dusk and midnight. Why?

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After midnight, skywatchers occupy a part of the globe that faces “forward” along Earth’s trajectory around the sun, so the meteoroids they see enter the atmosphere at a relatively high velocity. Between dusk and midnight we are facing “backward,” so the meteors we observe are catching up with us and enter the atmosphere at a lower speed. The faster a meteor travels through the atmosphere, the brighter it appears.

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August 18, 2015August 30, 2015 | Puzzles · Science & Math

Black and White

ropet chess problem

By Ivan Pavlovich Ropet. White to mate in two moves.

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1. Nf4! (threatening 2. Rd5#) Kxd4 2.Bf6# From the St. Petersburg New Times, 1899.

August 16, 2015August 30, 2015 | Puzzles

Podcast Episode 69: Lateral Thinking Puzzles

Here are four new lateral thinking puzzles to test your wits! Solve along with us as we explore some strange situations using only yes-or-no questions.

See full show notes …

August 10, 2015October 24, 2017 | Podcast · Puzzles

Black and White

legentil chess problem

By Georges Legentil. White to mate in two moves.

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1. Nc4! stops the pawns, and the queen will mate. From Journal de Rouen, March 4, 1911.

August 3, 2015August 16, 2015 | Puzzles

Knife Act

knife act - problem

I have just baked a rectangular cake when my wife comes home and barbarically cuts out a piece for herself. The piece she cuts is rectangular, but it’s not in any convenient proportion to the rest of the cake, and its sides aren’t even parallel to the cake’s sides. I want to divide the remaining cake into two equal-sized halves with a single straight cut. How can I do it?

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A line drawn through the center of a rectangle, in any direction, will cut it evenly in two. So a line that passes through both the center of the cake and the center of the removed rectangle will divide the remaining cake into equal halves, regardless of the proportions involved or the hole’s orientation. You can find the center of each rectangle by noting the intersection of its diagonals.