Brain Teasers 9 - Puzzle Prime

Toasting Bread

Section: Brain Teasers Category: Deduction

Difficulty: Medium

Your toaster is broken, so you decide to toast your bread in a pan. The pan can hold three slices of bread at a time and takes 1 minute to toast one of their sides. How much time would it take you to toast four slices of bread on both sides using the pan?

SOLUTION

It would take you 2 minutes and 40 seconds. Label the slices with A, B, C, D, their top sides A1, B1, C1, D1, and their bottom sides A2, B2, C2, D2.

Toast A1, B1, C1 for 40 seconds.
Toast A2, B2, D1 for 40 seconds.
Toast A1, C2, D2 for 20 seconds.
Toast A2, C2, D2 for 20 seconds.
Toast B1, C1, D1 for 20 seconds.
Toast B2, C2, D2 for 20 seconds.

Unknown Author March 1, 2023

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100 Guests in 99 Rooms

Section: Brain Teasers Category: Deduction

Difficulty: Easy

One hundred people entered a hotel that had 99 rooms, and each of them asked for their own room. In order to solve the problem, the bellboy did the following:

He asked the 100th guest to wait for a while with the 1st guest in room number 1, so that there were 2 guests inside. Then he took the 3rd guest to room number 2, the 4th guest to room number 3, and so on, until finally taking the 99th guest to room number 98. At the end he returned to room number 1 and took the 100th guest to room number 99, which was still vacant.

How could everybody get their own room?

SOLUTION

The two people who were taken to room number 1 were guest 1 and guest 100. Thus, the 2nd guest ended up without a room.

Unknown Author February 22, 2023

2 Comments

Died on the Fourth of July

Section: Brain Teasers Category: Deduction

Difficulty: Medium

During a trivia night, the following question appeared:

“Among the first five US presidents, Washington, Adams, Jefferson, Madison, and Monroe, there were 3 who died on the fourth of July. Can you guess which ones?”

After nobody answered the question, the following hint was given:

“These three presidents were consecutive ones.”

Then, all contestants immediately managed to answer the question. Can you?

SOLUTION

Because of the way the question was worded, it was clear that the fifth president, James Monroe, was one of them. Otherwise, the trivia question would have been “among the first four US presidents” instead of “among the first five”. Since the three presidents that died on fourth of July were consecutive ones, they were Jefferson, Madison, and Monroe.

Unknown Author February 16, 2023

2 Comments

Limbs

Section: Brain Teasers Category: Deduction

Difficulty: Advanced

Partition the grid into disjoint “creatures”, according to the following rules:

Each creature is defined as a shape of 4 connected branches that are each 1 cell wide.
For each creature, one of the branches ends up with a HEAD (always clued) and the other three branches end up with LIMBS (whenever clued, their directions matter).
A creature can never occupy a 2×2 region of cells and can never touch itself.

Examine the first example, then solve the other three puzzles.

SOLUTION

The solutions are shown below.

Blaž Urban February 10, 2023

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Do Not Add E

Section: Brain Teasers Category: Insight

Difficulty: Medium

Add a single letter at the end to create a meaningful word. You CANNOT add the letter E.

S E Q U E N C _

SOLUTION

You should add the letter F above the underscore to create the letter E and get the word SEQEUNCE.

Unknown Author February 7, 2023

1 Comment

1 2 3 4 5 ?

Section: Brain Teasers Category: Insight

Difficulty: Medium

Can you guess what the question mark should be replaced with? The answer is not 6.

1	3	5
2	4	?

SOLUTION

The missing symbol is R, as in a car’s gears.

Unknown Author February 4, 2023

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Mammals in Cages

Section: Brain Teasers Category: Insight

Difficulty: Easy

You walk into a room where there are three mammals held in cages:

a trained dog doing tricks
a monkey playing with blocks
a lab rat traversing a maze

Which is the most intelligent mammal in the room?

SOLUTION

The answer is… YOU.

Unknown Author January 28, 2023

1 Comment

Rabbits, Owls, and Bears

Section: Brain Teasers Category: Insight

Difficulty: Medium

If:

RABBIT → FROG
OWL → WOLF
BEAR → SHEEP
MOOSE → COW

then BUCK → ?

SOLUTION

The answer is CHICKEN.

RABBIT sounds like the noise a FROG makes, OWL sounds like the noise a WOLF makes, BEAR sounds like the noise a SHEEP makes, and MOOSE sounds like the noise a COW makes. Since BUCK sounds like the noise a CHICKEN makes, that’s the answer.

Unknown Author January 25, 2023

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Get the Car

Section: Brain Teasers Category: Deduction

Difficulty: Medium

If you make a CORRECT statement, you will get either a lollipop or a chewing gum. If you make a FALSE statement, you will get either a chocolate or a car. What statement should you make in order to get the car?

SOLUTION

You should say “I will receive a chocolate”. This statement cannot be correct, since if it was, you would get a lollipop or a chewing gum, not a chocolate. Therefore, you will get the car.

Raymond Smullyan January 22, 2023

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Sum Up to 999

Section: Brain Teasers Category: Mathematics

Difficulty: Advanced Tags: Cryptarithm

Can you find a triple of three-digit numbers that sum up to 999 and collectively contain all digits from 1 to 9 exactly once? How many such triples are there? What if the sum was 1000?

SOLUTION

There are exactly 180 such triples that sum up to 999 and none that sum up to 1000.

In order to see that, notice that the sum of the first digits of the numbers can be no more than 9. Since the sum of all digits is 45, the sum of the middle and the sum of the last digits should be both no more than 9+8+7=24, and no less than 45-9-24=12. We then see that the sum of the last digits should be exactly 19 and the sum of the middle digits should be exactly 18. The sum of the first digits should be 45-19-18=8.

There are 2 ways to get 8 using unique digits from 1 to 9: 1+2+5 and 1+3+4.

If the first digits are {1, 2, 5}, the options for the middle digits are {3, 6, 9}, {3, 7, 8}, and {4, 6, 8}. The last digits end up {4, 7, 8}, {4, 6, 9}, and {3, 7, 9} respectively.
If the first digits are {1, 3, 4}, the options for the middle digits are {2, 7, 9} and {5, 6, 7}. The last digits end up {5, 6, 8} and {2, 8, 9} respectively.

Since the set of the first digits, the set of the middle digits, and the set of the last digits of the numbers can be permuted in 6 ways each, we get a total of 5×6×6×6=1080 solutions, or 180 up to permutation of the 3 three-digit numbers.

In order to see that we cannot get a sum of 1000, we note that since the sum of the digits from 1 to 9 is divisible by 9, then the sum of the 3 three-digit numbers should be divisible by 9 as well. Since 1000 is not divisible by 9, the statement follows.

Unknown Author January 16, 2023

17 Comments