Puzzle Archives - Puzzle Prime

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

0 Comments

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

0 Comments

Hidden Objects Birds

Section: Casual Puzzles Category: Hidden Objects

Difficulty: Medium

Can you find the bird with the party hat?

SOLUTION

The solution is shown below.

Jose Valor February 1, 2023

2 Comments

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

0 Comments

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

0 Comments

Pun Riddles

Section: Casual Puzzles Category: Riddle

Difficulty: Medium

Why do people go to the corner of the room when they are cold?
Why was everyone afraid of Albert Einstein’s brother, Frank?
What subject does a witch teach at school?
What room can’t a skeleton enter?
What rock group has only four members and none of them sing?
What has two butts and kills people?
How many tickles does it take to make a squid laugh?
What do you call a squad of babies?
What is a geologist’s favorite music genre?
What’s blue and not very heavy?

SOLUTION

Because it is 90 degrees there.
Because he was Frank-Einstein, a monster.
Spell-ing.
The living room.
Mount Rushmore.
An assassin.
Ten-tickles.
An infantry.
Rock.
Light blue.

Unknown Author January 19, 2023

0 Comments

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

FEATURED

A Broken Circle

Section: Brain Teasers Category: Mathematics

Difficulty: Expert Tags: Featured

There are N points on a circle. If we draw all the chords connecting these points and no three of them intersect at the same point, in how many parts will the interior of the circle get broken?

For example, when N is equal to 1, 2, 3, 4, and 5, we get 1, 2, 4, 8, and 16 parts respectively.

SOLUTION

The answer, somewhat surprisingly, is not 2ᴺ⁻¹, but 1 + N(N-1)/2 + N(N-1)(N-2)(N-3)/24.

In order to see that, we start with a single sector, the interior of the circle, and keep successively drawing chords. Every time we draw a new chord, we increase the number of parts by 1 and then add 1 extra part for each intersection with previously drawn chords.

Therefore, the total number of parts at the end will be:

1 + the number of the chords + the number of the intersections of the chords

Each chord is determined by its 2 endpoints and therefore the number of chords is N(N-1)/2.

Each intersection is determined by the 4 endpoints of the two intersecting chords and therefore the number of intersections is N(N-1)(N-2)(N-3)/4!.

Unknown Author January 13, 2023

0 Comments