Brain Teasers 45 - Puzzle Prime

Abbreviations

Section: Brain Teasers Category: Insight

Difficulty: Advanced

Can you find what the following abbreviations stand for?

24 H in a D = 24 Hours in a Day
26 L of the A = ???
7 D of the W = ???
7 W of the W = ???
12 S of the Z = ???
66 B of the B = ???
52 C in a P (W J) = ???
13 S in the U S F = ???
18 H on a G C = ???
39 B of the O T = ???
5 T on a F = ???
90 D in a R A = ???
3 B M (S H T R) = ???
32 is the T in D F at which W F = ???
15 P in a R T = ???
3 W on a T = ???
100 C in a R = ???
11 P in a F (S) T = ???
12 M in a Y = ???
13 is U F S = ???
8 T on a O = ???
29 D in F in a L Y = ???
27 B in the N T = ???
365 D in a Y = ???
13 L in a B D = ???
52 W in a Y = ???
9 L of a C = ???
60 M in a H = ???
23 P of C in the H B = ???
64 S on a C B = ???
9 P in S A = ???
6 B to an O in C = ???
1000 Y in a M = ???
15 M on a D M C = ???

SOLUTION

24 H in a D = 24 Hours in a Day
26 L of the A = 26 Letters of the Alphabet
7 D of the W = 7 Days of the Week
7 W of the W = 7 Wonders of the World
12 S of the Z = 12 Signs of the Zodiac
66 B of the B = 66 Books of the Bible
52 C in a P (W J) = 52 Cards in a Pack (Without Jokers)
13 S in the U S F = 13 Stripes in the United States Flag
18 H on a G C = 18 Holes on a Golf Course
39 B of the O T = 39 Books of the Old Testament
5 T on a F = 5 Toes on a Foot
90 D in a R A = 90 Degrees in a Right Angle
3 B M (S H T R) = 3 Blind Mice (See How They Run)
32 is the T in D F at which W F = 32 Degrees is the Temperature in Fahrenheit at which Water Freezes
15 P in a R T = 15 Players in a Rugby Team
3 W on a T = 3 Wheels on a Tricycle
100 C in a R = 100 Cents in a Rand
11 P in a F (S) T = 11 Players in a Football (Soccer) Team
12 M in a Y = 12 Months in a Year
13 is U F S = 13 is Unlucky For Some
8 T on an O = 8 Tentacles on an Octopus
29 D in F in a L Y = 29 Days in February in a Leap Year
27 B in the N T = 27 Books in the New Testament
365 D in a Y = 365 Days in a Year
13 L in a B D = 13 Loaves in a Baker’s Dozen
52 W in a Y = 52 Weeks in a Year
9 L of a C = 9 Lives of a Cat
60 M in an H = 60 Minutes in an Hour
23 P of C in the H B = 23 Pairs of Chromosomes in the Human Body
64 S on a C B = 64 Squares on a Chess Board
9 P in S A = 9 Provinces in South Africa
6 B to an O in C = 6 Balls to an Over in Cricket
1000 Y in a M = 1000 Years in a Millennium
15 M on a D M C = 15 Men on a Dead Man’s Chest

Unknown Author August 10, 2018

3 Comments

Height Arrangement

Section: Brain Teasers Category: Mathematics

Difficulty: Hard

Suppose you have 10 people with different heights in one row. Show that you can always remove 6 of them, so that the remaining 4 are arranged with respect to their heights (either increasing or decreasing).

SOLUTION

Mark the first person with number 1. Look for the next person after him, who is taller, and also mark him with number 1. Then look for the first person after the second one, who is taller, and also mark him with number 1. If you find a fourth one, then you already got the four people you are looking for.

If not, mark the first unmarked person with number 2. Look for the next unmarked person after him, who is taller, and also mark him with number 2. Continue with the procedure, until you either find 4 people in the line, whose heights are increasing, or have people who are marked with numbers 1, 2, 3 and 4.

Now pick a person, who is marked with number 4. Then look for the closest person on the left, who is marked with number 3, pick him up. He will be taller, because otherwise the first person would have been labeled 3 as well. Similarly, look for the closest person, marked with 2, on the left of the last one, pick him up. Repeat this once again and you will find 4 people in the line, whose heights are decreasing.

Unknown Author August 7, 2018

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The Stolen Tools

Section: Brain Teasers Category: Detective

Difficulty: Advanced

Tools were stolen from a construction site. Max Mouse found footprints and a tire track, leading him to believe there were two thieves – one walking and the other riding a bike. Even though Slylock Fox believes both tracks are related to the robbery, he suspects there was only one thief. Why?

SOLUTION

The tire track cannot be from a bike. The tracks were left by one thief pushing a wheelbarrow, full of stolen tools.

Bob Weber July 28, 2018

5 Comments

Reti’s Magic

Section: Brain Teasers Category: Chess

Difficulty: Medium

It is White’s move next. Is this game a win for Black or a draw?

SOLUTION

The game is a draw. The first two moves of White are Kg7 and Kf6. If Black moves the king twice in the meantime, then White can get to the pawn on the h-file and take it. If Black moves the king once, then White plays Ke5. If Black moves the king again, White can take the pawn on the h-file. Otherwise, White plays Kd6 and can promote his pawn right after Black promotes his. Finally, if after Kg7 and Kf6 Black moves the pawn twice, then White plays Ke7, and once again can promote his pawn right after Black promotes his.

Richard Réti July 25, 2018

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The Pony Puzzle

Section: Brain Teasers Category: Practical

Difficulty: Hard

Print the image below, cut out the six parts of the pony, and then rearrange them so that a picture of a horse (not a pony) appears.

SOLUTION

The horse is formed in the empty space between the pony parts.

Sam Loyd July 7, 2018

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Trolls and Cakes

Section: Brain Teasers Category: Deduction

Difficulty: Medium

You are on your way to visit your Grandma, who lives at the end of the valley. It’s her birthday, and you want to give her the cakes you’ve made.

Between your house and her house, you have to cross 7 bridges, and as it goes in the land of make-believe, there is a troll under every bridge! Each troll, quite rightly, insists that you pay a troll toll. Before you can cross their bridge, you have to give them half of the cakes you are carrying, but as they are kind trolls, they each give you back a single cake.

How many cakes do you have to leave home with to make sure that you arrive at Grandma’s with exactly 2 cakes?

SOLUTION

You leave with 2 cakes. Every time you cross a bridge, you give one of them to a troll, and then get it back. Eventually, you will arrive at your grandma with exactly 2 cakes.

Unknown Author June 27, 2018

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The Candy Shop

Section: Brain Teasers Category: Deduction

Difficulty: Medium

A candy shop lets children exchange 3 chocolate wrappers for a brand new chocolate. Willy is walking around town collecting chocolate wrappers from people. How many wrappers must he collect in order to eat 10 chocolates?

SOLUTION

He needs only 21 wrappers. He uses them to get 7 chocolates. After he eats them, he is left with 7 wrappers, which uses to get 2 more chocolates. After he eats these, he is left with 3 wrappers, which are enough to get one more chocolate and make them 10 in total.

Unknown Author June 18, 2018

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Professor Al’s Books

Section: Brain Teasers Category: Insight

Difficulty: Medium

Professor Al has put the “Lord of the Rings” trilogy books on his shelf in order, next to each other. The books are hard copies, with pages which are 1/100in thick and covers which are 1/8in thick. A worm is eating its way from the first page of the first volume to the last page of the third volume. If each of the volumes contains 400 pages, how long this distance is?

SOLUTION

The first page of the first volume and the last page of the third volume are separated only by the second volume and the extra 2 book covers. Therefore the distance is 4in + 0.5in = 4.5 inches long.

Unknown Author June 17, 2018

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London Escalators

Section: Brain Teasers Category: Lateral

Difficulty: Advanced

In London, many Underground tube stations have two escalators going up, but just one going down. Why?

SOLUTION

This is because when people leave the train, they pack into groups, whereas when they go to catch the train, their flow is evener.

Unknown Author June 10, 2018

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King Octopus and His Servants

Section: Brain Teasers Category: Deduction

Difficulty: Medium

King Octopus has servants with 6, 7, or 8 legs. The servants with 7 legs always lie, and the servants with 6 or 8 legs always tell the truth. One day four of the king’s servants had the following conversation:

“We together have 28 legs,” said the first octopus.
“We together have 27 legs,” said the second octopus.
“We together have 26 legs,” said the third octopus.
“We together have 25 legs,” said the fourth octopus.

Which of the four servants told the truth?

SOLUTION

If all four octopuses lied, then their total number of legs must be 28, which is impossible. Therefore exactly one of them said the truth, and the other three had 7 legs each. Since the truthful octopus must have 6 or 8 legs, and 21 + 8 = 29, we see that it has exactly 6 legs, and therefore it is the second one.

Unknown Author June 5, 2018

4 Comments