Bulmaca Takvimleri

A pandemic is spreading across an n × n grid. Each tile gets “infected” if at least two of its four neighbours are infected. What is the minimum number of infected squares required initially, so that the pandemic could spread to eventually cover the the entire grid?

Please sign in to see the solution.

Six circles with radius 1 are arranged in a regular hexagon. What is the area of the dark, enclosed space?

Please sign in to see the solution.

I write down the digits from 1 to 9 in a random order. What is the probability that the resulting number is divisible by 11?

Please sign in to see the solution.

How many squares can you draw with their vertices on a grid?

How about a more general grid?

Please sign in to see the solution.

How often, on average, do you have to roll a die, to see all six sides come up at least once?

Please sign in to see the solution.

An isosceles triangle is placed inside a square. We draw the incircle of the isosceles triangle, and one of the other triangles on either side. What is the ratio of the radii of these two circles?

Please sign in to see the solution.

The numbers a, b, c, d and e are positive integers so that

What is the maximum possible value of any of these integers?

Please sign in to see the solution.

Can you place one star in every row, column and region? Stars can’t be adjacent, even diagonally.

Please sign in to see the solution.

This shape consists of three congruent, right-angled, isosceles triangles. Can you divide it into four congruent regions?

“Congruent” means that the four regions need to have the same size and shape.

Please sign in to see the solution.

Knights always tell the truth and knaves always lie.

You are approached by two of them, and one says “we are both knaves”. Who are they actually?

Please sign in to see the solution.

Continue this sequence:

23, 21, 24, 19, 26, 15, 28, 11, 30, 7, ?, ?

Please sign in to see the solution.

What is the radius of the largest circle that can be drawn on a chess board, so that its circumference lies entirely on black squares?

Each square has side length 2.

Please sign in to see the solution.

How far apart are the centres of these two circles with radius 1, if all three shaded regions have the same area?

Please sign in to see the solution.

Can you divide this chessboard into four congruent “kingdoms” that each contain one of the kings? (The kingdoms must have exactly the same size and shape.)

The kings are placed in row 5 and columns 4, 5, 6 and 7, and cannot be moved. The kingdoms also have to be orthogonally connected (they can't consist of multiple disjoint regions).

This puzzle has been featured in The Guardian

Please sign in to see the solution.

A box contains 100 balls labelled from 1 to 100.

You select 10 balls at random. What is the expected value of the largest number you picked?

Please sign in to see the solution.

Place the numbers from 1 to 12 into these circles, arranged in a six-sided star, so that the sum along all six lines is the same.

Please sign in to see the solution.

A white cube is painted black on its outside and then cut into 27 small pieces. The pieces are mixed and randomly reassembled into another cube.

What proportion of the surface area of the new cube is expected to still be black?

Please sign in to see the solution.

A 3-4-5 triangle lies inside a square. What is the area of the square?

Please sign in to see the solution.

Place the digits from 1 to 8 in these boxes, so that consecutive digits are not adjacent (even diagonally).

Please sign in to see the solution.

How often, on average, do you have to flip a (fair) coin, until you get 10 consecutive heads?

Please sign in to see the solution.

Two trains with 2 and 3 carriages are travelling in opposite directions on the same track. There is a siding, but it only has space for one carriage or locomotive. How can the trains pass each other?

Locomotives can drive forwards and backwards, and attach to carriages on either side.

Please sign in to see the solution.

In this triangle, the length of all three sides and its height are four consecutive integers. What is the area of the triangle?

Please sign in to see the solution.

Two 3-digit numbers sum to a third number with 3 digits.

The digits of all three numbers are permutations of each other. What are these numbers?

None of the digits are 0s.

Please sign in to see the solution.

What is the average distance between two points picked randomly on the circumference of a circle?

Note: This problem requires calculus.

Please sign in to see the solution.

This is the most efficient way to place three congruent squares in an equilateral triangle. What proportion of the triangle is shaded?

Please sign in to see the solution.

You pick three random points on a circle. What is the probability that the resulting triangle contains the center of the circle?

The points are picked uniformly at random, along the circumference of the circle.

Please sign in to see the solution.

Can you measure exactly 15 minutes using nothing but an 11-minute hourglass and a 7-minute hourglass?

Please sign in to see the solution.

What proportion of a square is closer to its centre than its edge?

This problem is surprisingly difficult and requires calculus.

Please sign in to see the solution.

What 4-digit number, when multiplied by 4, reverses the order of its digits?

ABCD × 4 = DCBA

This puzzle has been featured in The Guardian

Please sign in to see the solution.

Can you place 18 black and 18 white tiles on a 6×6 board, so that there are no “squares” with their four corners having the same colour?

From Martin Gardner’s “Sphere Packing, Lewis Carroll, and Reversi”

Please sign in to see the solution.

Three geysers A, B and C in a national park erupt every 1, 2 and 3 hours respectively. You just arrived: what is the probability that you will see geyser A erupt first?

Inspired by The Riddler on FiveThirtyEight

Please sign in to see the solution.

What’s the angle between these two congruent equilateral triangles?

Inspired by Catriona Shearer

Please sign in to see the solution.

Continue this sequence:

6, 10, 14, 15, 21, 22, 26, 33, 34, 35, …

Please sign in to see the solution.

Scientists are studying a micro-organism, starting with a single cell. Every day, each cell either splits in two (with probability p), or it dies. What is the probability that the entire organism dies eventually?

Please sign in to see the solution.

Can you arrange the seven Tetrominoes in a 7×4 rectangle, with no gaps or overlaps?

Please sign in to see the solution.

You have 10 cans of peas. All peas weigh 1 gram, except for one can with peas that weigh 0.9 grams. How often do you need to use a scale to find this lighter can?

Please sign in to see the solution.

Can the locomotive L switch the position of the two wagons and end up where it started? Only the locomotive can fit under the bridge.

From Martin Gardner’s “Sphere Packing, Lewis Carroll, and Reversi”

Please sign in to see the solution.

25 frogs are sitting in a 5×5 grid. Every frog jumps into an adjacent square (left, right, up or down). What is the largest number of squares that could become empty?

This puzzle has been featured in The Guardian

From the Netherlands Junior Maths Olympiad

Please sign in to see the solution.

I repeatedly toss a fair coin and record the outcome. What is the probability that the sequence “HHH” occurs before “THH”?

Please sign in to see the solution.

A castle is surrounded by a 5 meter wide, rectangular moat. Can you cross it using nothing except two planks that are 4.8 meters long?

This puzzle has been featured in The Guardian

Please sign in to see the solution.

What’s the value of x?

x^xxxx… = 2

Please sign in to see the solution.

Can you plant 7 trees so that there are 6 straight lines containing 3 trees each?

Please sign in to see the solution.

How many ways are there to distribute 10 identical cookies between five different kids?

Kids don’t need to receive the same number of, or any, cookies.

Please sign in to see the solution.

What is the least number of integers needed, so that any of these could be true?

Median < Mean < Mode
Median < Mode < Mean
Mode < Median < Mean
Mode < Mean < Median
Mean < Mode < Median
Mean < Median < Mode

The mode has to be well-defined, so you can’t have two different integers both appear the most number of times. For example, the set {1, 2, 2, 3, 3} doesn’t have a well-defined mode, because both 2 and 3 appear twice.

Please sign in to see the solution.

Rearrange these numbers and symbols to make a true equation:

2 3 4 5 + =

Please sign in to see the solution.

There are 100 strings in a bag. You randomly pick two ends and tie them together, until there are no free ends left. What is the expected number of loops you will create?

Please sign in to see the solution.

A semicircle lies inside a square. What proportion of the square is shaded?

Please sign in to see the solution.

How many ways are there to tile a rectangle of size 2×10 with dominoes?

Dominoes are tiles of size 2×1 and can be placed horizontally or vertically. All dominoes need to be contained within the board, and there can’t be any gaps. Can you find a general answer for a board of size 2×n? What about a board of size 3×n?

Please sign in to see the solution.

How many triangles are there?

This puzzle has been featured in The Guardian

Please sign in to see the solution.

A circle of radius 1 rolls around the inside of another circle of radius 3. What is the length of the path traced out by a point on the small circle?

Please sign in to see the solution.

I’m thinking about a large integer.

• It is divisible by 1.
• It is divisible by 2.
• It is divisible by 3.
• …
• It is divisible by 30.

Exactly two consecutive of these statements are wrong. Which ones?

This puzzle has been featured in The Guardian

Please sign in to see the solution.

You have 9 balls, one of which is slightly heavier than the others.

How often do you need to weigh two groups of balls, to find the odd one out?

Please sign in to see the solution.

Two equilateral triangles are drawn inside a square. What is the area of the smaller triangle?

Please sign in to see the solution.

A cinema announces a special deal: the first person in the queue to have the same birthday as someone in front of them, will get a free ticket.

Which position in the queue is the best?

Please sign in to see the solution.

At a party, every guest shook hands with everyone else. There were 66 Handshakes in total. How many guests attended the party?

Please sign in to see the solution.

Four cities form the vertices of a square. What is the shortest way to connect them with each other using railroad tracks?

The tracks may intersect, and you can add “junctions”. Hint: Two diagonals is not the shortest path!

Please sign in to see the solution.

This is a Magic Sum Square, where the sum of every row, column and diagonal is 15. Can you find a Magic Product Square?

Please sign in to see the solution.

Can you cut this obtuse triangle into smaller, acute triangles? If so, how many cuts do you need?

Note that a right angle is neither acute nor obtuse!

Please sign in to see the solution.

A cylindrical hole of length 6cm has been drilled through the center of a solid sphere. What is the volume of the remaining sphere?

Please sign in to see the solution.

When placing 5 queens on a 5µ5 chess board, what is the maxiumum number of fields you can leave “unattacked” (no queen can reach them within one turn)?

This puzzle has been featured in The Guardian

Please sign in to see the solution.

Can you insert mathematical operators, to make this equation true?

0 0 0 0 0 = 120

Please sign in to see the solution.

Where did the missing square go?

Please sign in to see the solution.

Continue this sequence:

5, 9, 15, 21, 39, 45, 69, 81, 99, 105, …

Please sign in to see the solution.

I’ll offer you $4 to play this game:

You have to toss a coin repeatedly, until it lands heads. Then you have to pay me back $1 for every toss.

Do you want to play?

Please sign in to see the solution.

You have two ropes that burn in exactly 60 minutes – but not neccessarily at a constant rate.

How can you measure 45 minutes?

Please sign in to see the solution.

A farmer has 300 bananas which he wants to sell at a market 100km away.

His camel can carry 100 bananas at once, and eats one banana per km.

What is the most bananas he can take to the market?

Please sign in to see the solution.

How many guards do you need for this museum, so that every corner can be watched?

Guards have 360° vision, but they cannot move.

Please sign in to see the solution.

Here you can see some examples of Trapezium Numbers. There is just one number between 1,000 and 2,000 that doesn’t form a trapezium. Which one?

Please sign in to see the solution.

Three ants are sitting at the corners of a triangle. Each ant picks one direction at random and starts walking. What is the probability that none of the ants collide?

This puzzle has been featured in The Guardian

Please sign in to see the solution.

You break a stick in two different places at random. What is the probability that the resulting three pieces form a triangle?

Please sign in to see the solution.

You have a large number of 5-cent stamps and 17-cent stamps. What is the largest cent value which you cannot make using a combination of these stamps?

Please sign in to see the solution.

Which regular polygons can be created using a ring of other regular polygons?

Please sign in to see the solution.

Can you make 24 using the numbers

3, 3, 8, 8,

and the operations

+ – × ÷ ( )

How many people do you need, so that the probability of two having the same birthday is at least 50%

A bag contains two green marbles and two blue marbles.

I pick two marbles at random and tell you that at least one is blue. What is the probability that the other one is also blue?

A small country contains 10 cities and 5 straight roads. Every road connects 4 different cities. Draw a map of the country!

How many guests do I have to invite to my christmas party, to be sure there will be at least 3 mutual friends, or 3 mutual strangers?

Any two guests are either strangers or friends.

In a dark room there’s a drawer with 10 red socks and 10 blue socks. How many socks do you have to take, to be sure to get a matching pair?

A market stall sells five different kinds of fruit.

I want to buy ten items. How many possible combinations are there?

How can I measure exactly 8 liters of water, using just one 11 liter and one 6 liter bucket?

People from the Town of Truth always tell the truth. People from the City of Lies always lie.

A guide from one of the cities is at the intersection and offers you a single question. What should you ask?

Place the numbers from 1 to 9 in the circles, so that the sum along all 3 sides is the same.

How many triangles are there?

You have to deliver five letters to five different houses, but the rain has erased all addresses. If you just distribute the letters randomly, what is the probability that everyone gets a wrong letter?

How many diagonals are there in a 10-gon?

What’s the smallest set of integers a, b, c, d and e that satisfy

a + b = c + d + e AND a² + b² = c² + d² + e²

All shapes have the same perimeter. Which one has the largest area?

Is the yellow dot on the inside or the ouside of this spiral?

Can you split this shape into two equal parts, with a single cut?

What’s next?

Where did the missing square go?

Find all pairs of numbers a and b that satisfy:

a + b = a × b = a / b.

Continue this sequence:

4, 6, 12, 18, 30, 42, 60, 72, 102, 108, …

What’s the area of the Koch Snowflake, where the largest triangle has side length 1?

Can you cover a 8×8 chessboard, with the two opposite corner tiles removed, entirely with dominoes (no gaps or overlaps)?

Rearrange these seven shapes to form the animals above!