Questions tagged [mathematics]

A puzzle strongly related to mathematical facts and objects, or whose solution needs serious mathematical arguments. General mathematics questions are off-topic but can be asked on Mathematics Stack Exchange.

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4
votes
0answers
58 views

Maximizing Product of Selected Cards

Jennifer is playing a game. The Ace through King of spades are taken from a standard playing deck and laid out facedown on the table. At any time, Jennifer can select two cards and reveal them, and ...
5
votes
1answer
101 views

Mathmatical equation answer [closed]

I think there must be a way to solve this but I can't get there Green + Blue = Yellow Red + Green = Purple Yellow - Purple = Red Red + Green + Blue = 9 I have made some progress And but I run ...
5
votes
1answer
178 views

Two cards which product is not a square

There are 100 cards on a table numbered 1,2,...,100. What is the maximum number of cards, which can be selected such that no two cards have a product, which is a perfect square? Example: you cannot ...
10
votes
4answers
1k views

Finding the hardest 5x5 grid for a blindfolded robot to solve

This puzzle is based on the framework described here: Controlling a robot blindfolded on a 9x9 grid Here is a quick summary. A robot is located somewhere on a grid, but you cannot see it. You can ...
2
votes
1answer
105 views

Placing three sets of cards Ace to 9 in a row

From an ordinary deck of playing cards remove cards ace to nine of any three suits (27 cards in all), and place them in a row so that between any 2 consecutive aces there is precisely 1 card, between ...
-1
votes
1answer
126 views

8-puzzle in 12 steps

This quiz is about the 8-puzzle. It is a board with 9 spaces. There are 8 tiles with the numbers 1 through 8. One space is empty (.). You slide the tiles around the ...
13
votes
8answers
4k views

Three people wearing hats

Ms. Doha gave hats with different non-zero single digits (two of which are factors of the third) to Ms. Haha, Ms. Lola and Mr. Hehe. The three of them can't see the digits on their own hat though they ...
0
votes
2answers
174 views

Controlling a robot blindfolded on ANY 2x2 grid

This puzzle is based on the framework described here: Controlling a robot blindfolded on a 9x9 grid Here is a quick summary. A robot is located somewhere on a grid, but you cannot see it. You can ...
39
votes
3answers
3k views

Controlling a robot blindfolded on a 9x9 grid

A robot is located somewhere inside a 9x9 grid shown below, but you don't know where it is. You can send commands to the robot to make it move one cell left, right, up or down. Shaded areas and edges ...
7
votes
2answers
1k views

Two congruent triangles

Each triangle has 6 basic determinants: 3 line segments and 3 angles. Is it possible to have two triangles, which have 5 of the basic determinants in common, but are not congruent?
0
votes
0answers
94 views

Factory Owner Brain Teaser [closed]

In his will, a factory owner leaves 80 000 dollars to be shared equally by his sons. But hours before his death, he disinherits several sons. The remaining boys then receive an extra 24 000 dollars ...
5
votes
1answer
94 views

How do I find the total sum of the numbers occupying three different regions of a $3 \times 3$ grid?

The problem is as follows: The following board must be completed with natural numbers from $1$ to $15$ with no repetitions allowed in such a way that the sum of the numbers on each of the three ...
-4
votes
1answer
132 views

A Sweetematical Puzzle [closed]

There are $n$ sweets in a bag, $6$ of the sweets are orange. The rest of the sweets are yellow. Hannah takes a random sweet from the bag She eats it. Hannah takes another random sweet from the bag ...
2
votes
0answers
110 views

Peaceable Bishops on a 10x10 grid version 2

Can you place 42 bishops with 6 bishops for each of the 7 colors on a 10x10 grid, such that no two bishops of different colors attack each other? Here are some similar questions: Peaceable Bishops ...
-3
votes
3answers
135 views

Uk math challenge puzzle [closed]

Hi I was trying this math challenge puzzle and I am wondering whether anyone here can work it out.! It is from a past paper a Uk Maths challenge
9
votes
2answers
2k views

Peaceable Bishops on an 10x10 grid

Can you place 22 red, 22 white and 22 black bishops on a 10x10 grid, such that no two bishops of different colours attack each other? Here is a similar question for 8x8 grid: Peaceable Bishops on an ...
6
votes
2answers
672 views

What is the name of AB×B×A=BBB puzzles?

Some puzzles goes as follows: Solve AB×B×A=BBB, where different letters denote different numbers and A and B are not zero. What is the name for these types of puzzles? Edit. I fixed my mistake in ...
7
votes
2answers
615 views

Peaceable Bishops on an 8x8 grid

Place an equal number of red, white and black bishops on a 8x8 chess grid, such that no two bishops of different colours attack each other. What is the largest number of bishops you can place? Bonus ...
3
votes
5answers
268 views

Find the number sequence, which number come next?

8 0 9 24 10 120 11 336 12 __ ? Hint:
10
votes
1answer
267 views

A puzzling currency

The main international airport in the Kingdom of Treisaria recently installed automatic currency exchange machines. You can insert banknotes from any of the major world currencies (dollars, euros, ...
5
votes
1answer
134 views

The grandest zoo in Appelhaken

In the magnificent country of Appelhaken there is a zoo. Not just any zoo, but a grand zoo, a magnificent zoo, called Appelhaken Grand Magnificent Magnificent Grand Grand Zoo. In this zoo there are ...
19
votes
6answers
8k views

What world is this where 6 + 6 = 10?

Upon traveling the world, I found myself in a peculiar place which was called Gauss. The locals there were a peculiar people, as I soon found out. I stopped to grab a bite to eat and learn about the ...
8
votes
1answer
163 views

The grandest bridge in Appelhaken [duplicate]

In the capital of the grand country of Appelhaken there is a plane garden containing four magnificent monuments. So magnificent are they that the country has a Law requiring that there must be a ...
2
votes
0answers
97 views

Diving a polygon into 6 equal regions [closed]

You are given a convex polygon, ie all its internal angles are less than 180 degrees. Prove that you can always draw three straight lines through a point inside this polygon, such that they divide it ...
13
votes
2answers
751 views

Hearts and Spades in a Row

From a deck of playing cards remove hearts ace to seven, and spades ace to seven. Now place them on a table in a row so that the number of cards between the two aces is 1, the number of cards ...
9
votes
2answers
613 views

Two button calculator part 2

A calculator has only 2 buttons. The first multiplies the current value by 2, the second divides it by 3 without a remainder (so 8 becomes 2). Can you use this calculator to reach every positive ...
-6
votes
1answer
99 views

Another how to kill 7 submarines

7 submarines are placed on an x, y grid - 0 to 111. They are located on whole numbered locations. Each submarine starts from any selected location with a given fixed speed and fixed direction, ...
5
votes
2answers
1k views

Euler's identity

Warning: this question requires knowledge of complex numbers. An Euler's identity is an identity, in which each of the following appears once and only once: the constant $0$: neutral element for ...
27
votes
6answers
4k views

A robot surviving on top of a 3x3 platform

A robot sits in the central square on top of a 3x3 platform. The robot can move up, down, left or right, but if it steps off the platform it will crash and die. You can preprogram the robot to make a ...
6
votes
1answer
950 views

Two super-button calculator

A calculator only has 2 buttons. The buttons are, however, very powerful: they are programmable buttons, i.e. you can pre-set them to be any function (meaning any map from $\mathbb{Z}$ to $\mathbb{Z}$)...
8
votes
3answers
349 views

Two button calculator

A calculator has only 2 buttons. The first multiplies the current value by 2, the second divides it by 3 without a remainder (so 8 becomes 2). Starting with 1 what is the least number of presses you ...
8
votes
3answers
1k views

Three button calculator part 2

A calculator only has 3 buttons. The first multiplies the current value by 3, the second adds 2 and the third subtracts 2. The calculator always starts with 0. What is the smallest positive even ...
9
votes
1answer
2k views

Three button calculator

A calculator has only 3 buttons. The first multiplies the current value by 3, the second adds 2 and the third subtracts 2. Starting with 0 what is the least number of presses you need to reach 100?
4
votes
1answer
225 views

Prime parallel rows for the first 20 numbers

Two positive integers can be joined with a straight segment if their sum is a prime and the segment doesn't intersect any other segments. What is the most number of pairs you can join if you can place ...
1
vote
1answer
155 views

How to kill 7 submarines

7 submarines are placed on an x, y grid - from negative infinity to positive infinity. They are located on whole numbered locations. Each submarine starts from a location with a given fixed speed and ...
2
votes
1answer
99 views

The first 10 prime butterflies

A prime butterfly is a set of three distinct numbers $a,b,c$, such that $a+b$ and $b+c$ are both primes. Can you divide numbers from 1 to 30 into 10 prime butterflies?
7
votes
2answers
202 views

Turning a fan on

I bought an air purifier which has [off, low, medium, high] settings and a single button. If it is on, the first button press activates the lights and subsequent presses increment the level with off ...
-5
votes
1answer
123 views

Find the next number in the weird sequence

The following sequence has been made using a specific pattern and the last number is kept secret. We have to find that number along with the pattern followed to make the sequence. 3, 11, 32, 71, ...
-2
votes
1answer
145 views

Missing Number Picture Puzzle

This is is logical reasoning puzzle in which your challenge is to find the relationship among the given numbers and then find the value of the missing number. Source: https://www.funwithpuzzles.com/...
6
votes
0answers
407 views

Locked Door Number Puzzle

I'm supposed to make a delivery to a crazed botanist. In case you're curious, the shipping manifest is: ...
9
votes
3answers
574 views

Discover the six-character password!

You are given several pieces of paper which are as follows: (Unfortunately, a textual rendering is very difficult with this puzzle, so if someone can offer a suggestion on how to do it, that would be ...
2
votes
0answers
186 views

Code Breaking ( Sort of )

So someone sent me this code breaking/riddle to solve and I got really confused on it. I do need help on it, The Code needs to come out into a Phrase ( group of words ) CLUE 1: 2210232013400 - ...
1
vote
0answers
71 views
0
votes
0answers
136 views

3 bags of coins, find which bag contains fake coins, doing only 1 weighing

Probably a very easy puzzle for you guys; my point is more a mathematical one. FYI, it was shown in an episode of Columbo. You have 3 bags of coins. Each bag contains 50 identical coins. Two bags ...
10
votes
5answers
452 views

2 fake coins from a pile of 30 coins

You need to find two fake coins from a pile of 30 coins. You know that a fake coin has a different weight to a real coin, but you don't know whether it is lighter or heavier. You also know that all ...
8
votes
10answers
5k views

There are polygons with only right angles which have an odd number of corners

One of the interesting myths about a certain building in our university is that it has 13 corners. One way to dismiss this claim is to point out that a polygon with right angles must have an even ...
5
votes
2answers
276 views

Two equal-sized lists that produce prime sums

Place one or more distinct numbers between 1 and 100 into the lists $𝑃$ and $𝑄$, such that they contain the same number of elements and any number from $𝑃$ added to any number from $𝑄$ gives a ...
15
votes
5answers
955 views

Dividing the first 20 numbers into 3 lists

Place every number from 1 to 20 into one of three lists $P$, $Q$ or $O$, such that any number from $P$ added to any number from $Q$ gives a prime. What is the fewest number of elements that can be in $...
7
votes
4answers
572 views

How to make the number 49?

You've to start with $1$ and can use each of the following operations at most once. You can do the following in any order you like: 1) Add $2$. 2) Add $3$. 3) Add $5$. 4) Multiply $2.$ 5) ...
7
votes
1answer
305 views

Density type puzzle 5

A puzzle in the spirit of this puzzle. I've tried to make it a bit tougher this time, though there are no distractions of any kind. Enjoy! Final answer: (4,5) Hint 1 Hint 2 Hint 3 Hint 4