Brain Teasers 51 - Puzzle Prime

NASA and the Meteor

Section: Brain Teasers Category: Mathematics

Difficulty: Advanced Tags: Geometry

NASA locates a meteor in outer space and concludes that it has either a cubical or spherical shape. In order to determine the exact shape, NASA lands a spacecraft on the meteor and lets a rover travel from the spacecraft to the opposite point on the planet. By measuring the relative position of the rover with respect to the spacecraft throughout its travel on the planet (in 3D coordinates), can NASA always determine the shape, no matter the route taken by the rover?

SOLUTION

The answer is NO.

The question is equivalent to analyzing the intersection of a cube and a sphere which share a common center. Thus the question gets reduced to figuring out whether such intersection, which is a curve, can connect two opposite points on the sphere/cube.

Let the edge of the cube has length 1. If you pick the radius of the sphere equal to √2/2, the intersection will consist of 6 circles inscribed in the sides of the cube. Then the rover can just move along these circles from one point to its opposite and NASA won’t be able to figure out the exact shape.

Remark: It is not hard to see that 2:√2 is the only edge-radius ratio, for which NASA can’t figure out the shape.

Unknown Author October 10, 2017

2 Comments

The Poisoned Glass

Section: Brain Teasers Category: Insight

Difficulty: Advanced

You are given 4 identical glasses, completely filled with transparent, odorless liquids. Three of the liquids are pure water, and the fourth is poison, which is slightly heavier. If the water glasses weigh 250 grams each, and the poisoned glass weighs 260 grams, how can you figure out which one is which, using a measuring scale just once?

SOLUTION

Empty the first glass, fill around 1/4th of it with liquid from the second glass, and the rest 3/4ths with liquid from the third glass. Then, measure the first and fourth glasses simultaneously. If their total weight is:

– 500 grams -> the first glass is (was) the poisoned one
– between 500 and 505 grams -> the second glass is the poisoned one
– between 505 and 510 grams -> the third glass is the poisoned one
– 510 grams -> the fourth glass is the poisoned one

Source:

Puzzling StackExchange

TSLF October 4, 2017

1 Comment

The Dark Bridge

Section: Brain Teasers Category: Deduction

Difficulty: Medium

Four friends are trying to cross a bridge in complete darkness, but have only one flashlight. They need respectively 1, 2, 7, and 10 minutes to cross the bridge, and if any three of them step on the bridge at the same time, it will collapse. How many minutes do they need at least in order for all of them to get to the other side?

SOLUTION

They need 17 minutes. Label the friends A (1min), B (2min), C (7min), D (10min). A and B cross the bridge, then A returns back with the flashlight. C and D cross the bridge, then B returns back with the flashlight. Finally, A and B cross the bridge.

In order to see that this is optimal, notice that when D crosses, he needs at least 10 minutes. If C crosses separately, this will make already 17 minutes in total. Therefore C and D must cross together, and A and B must be at that time on the two opposite sides of the bridge. From here it is easy to conclude that the friends indeed need at least 17 minutes.

Unknown Author October 1, 2017

1 Comment

Queen’s Death

Section: Brain Teasers Category: Chess

Difficulty: Hard

On which spot was the white queen captured?

SOLUTION

Since the pawns on e6 and h6 have taken 2 of the White’s pieces, and the only two white pieces which could get there are the knight and the queen, the answer is one of these two squares. Similarly, the pawn on b3 should have taken the Black’s c8 bishop, and this should have happened before the White’s queen was taken. Therefore first the white knight was taken on e6, then the black bishop on b3, and finally the white queen on h6.

Raymond Smullyan September 28, 2017

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Chiming Wall Clock

Section: Brain Teasers Category: Deduction

Difficulty: Medium

Your grandma’s wall clock chimes the appropriate number of times at every whole hour, and also once every 15 minutes. If you hear the wall clock chime once, how much more time do you need to figure out what the time is, without looking at it?

SOLUTION

1 hour and 30 minutes. The wall clock will chime once at 12:15, 12:30, 12:45, 1:00, 1:15, 1:30, 1:45. If you hear 7 consecutive times just 1 chime, then the time is 1:45. If you hear less than that, you will easily find what the time is once again.

Unknown Author September 22, 2017

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Light It Up

Section: Brain Teasers Category: Insight

Difficulty: Easy

If you have one match and enter a room in which there is a stove, a kerosine lamp, and an oil burner, what will you light up first?

SOLUTION

The match.

Unknown Author September 19, 2017

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4 builders, 4 houses

Section: Brain Teasers Category: Deduction

Difficulty: Easy

If it takes four months for four builders to build four houses, how many months it will take for two builders to build two houses?

SOLUTION

It will still take four months (not two).

Unknown Author September 16, 2017

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Deadly Vodka

Section: Brain Teasers Category: Lateral

Difficulty: Hard

Two politicians go to a bar and order two glasses of vodka on the rocks. The first politician quickly empties his glass, then orders a second one, a third one… The second politician patiently drinks his own vodka, but about 20 minutes later, he drops down dead. The police discovered that the barman tried to assassinate both politicians, but how come the second one died and the first one lived?

SOLUTION

The poison was in the ice cubes, so the second politician drank them when they melted in his drink.

Unknown Author September 13, 2017

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Careless Truck Driver

Section: Brain Teasers Category: Lateral

Difficulty: Medium

A truck driver was going the opposite way on a one-way street, but no policeman stopped him, even though few of them saw what he was doing. Why?

SOLUTION

Because the truck driver was just a pedestrian on that day, not driving his truck.

Unknown Author September 10, 2017

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Puddle of Water

Section: Brain Teasers Category: Lateral

Difficulty: Medium

A man is found in a room without any windows, with just one door which is locked from the inside. The man is hanging from a ceiling fan, dead, 4 feet above the floor. The room is completely empty, except for the man, the fan, and a puddle of water on the floor. How did the man die?

SOLUTION

The man used a block of ice so that he could hang himself, and then the ice melted into the puddle of water.

Unknown Author September 7, 2017

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