Questions tagged [mathematics]

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

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4
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0answers
53 views

A Perfect Diamond of Numbers

A diamond of numbers is an arrangement of circles in the shape of a trapezoid (see figure) in which the number in any circle above its central (longest) row is the sum of the two numbers in the ...
14
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1answer
324 views

Coin Flipping Puzzle

This is a repost from my post at Math Stack Exchange 2 criminals A and B, were recently captured and brought to prison. They were then locked in two separate rooms. Known for being exceedingly smart, ...
2
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1answer
198 views
+50

Squares and chords in a circle

The whole numbers 1 to 2n are placed in order around a circle. For which n is it possible to draw n non-intersecting chords (one from each number) such that each of them joins two numbers whose sum ...
18
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3answers
2k views

The Thieves and the Gold Bars

Two thieves (Rod and Lia) carry out a big heist and steal 16 gold bars. They get away in their car when they run into a bad accident and the car is completely wrecked. Luckily they survive with their ...
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0answers
68 views

Who owes what and to whom [closed]

There are 3 people involved: A M and H The total cost of a bar bill is £379.00 A and M each stayed in the hotel for 7 nights each H stayed for 4 nights A paid £283.00 M paid £96.00 H paid 0 If the bar ...
3
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2answers
710 views

Most points on a circle

What is the most number of integer lattice points that lie on the circumference of a single circle whose radius is 80 or less? Please no computer computations.
12
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3answers
975 views

Tiling with Js and Ls

In this puzzle you must tile the plane with identically sized colored L and J tetraminos. To start I will place two of them like so: Your task will be to tile the entire rest of the plane meeting ...
0
votes
1answer
211 views

What number comes next in 2, 4, 5, 3, 10, …

2, 4, 5, 3, 10, 11, 13, 7, 5, 28, 29, 31, 35, ??? I tried plugging it into Wolfram Alpha which couldn't find any pattern, and I'm still not too sure how to determine what number comes next. Any ideas?...
4
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1answer
135 views

Finding the path on a hexagonal playground?

Ben is at school playground. The playground is a special playground though: Its in a form of a hexagonal grid, and each hexagonal spot has a number. Ben loved the playground, and was even more eager ...
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0answers
110 views

Smallest Autonumerogram

An autonumerogram consists of digits and their counts, counts always appeared immediately before the corresponding digit, and no digit and its count were repeated or overlapped. For example: 22 has 2 ...
5
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2answers
435 views

Catch the angel in less than 7 units of time

The devil has trapped the angel in a regular hexagram of firewalls. The perimeter of the hexagram is 12. The devil starts at the apex of the hexagram. can move at speed $1$ to leave a trajectory of ...
7
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7answers
6k views

Prove that sin(x) ≥ x/2, but without calculus!

Important Note: After when this puzzle was posted, many people pointed out errors and improvements that could be made. I also noticed many flaws, so the post once had gone through drastic changes. ...
3
votes
1answer
191 views

How can the swear jar's balance sheet be recreated?

The boss, fed up with the scurrilous language flying around the office, instituted a "swear jar": employees overheard swearing would have to pay arbitrary fines, while those complimenting or ...
4
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1answer
623 views

Guess the algorithm

Here you are seeing part of a pattern I created with my computer. Can you either reproduce it or describe the algorithm I used?
10
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0answers
377 views

How long can you survive at the devil's playground?

The devil has trapped you in his playground. The devil knows that you can't cross over the burning boundary of his circle, so he allows you to choose a position within the circle before he starts to ...
30
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2answers
3k views

Sum of the first 86 square roots

Without using a calculator or a computer, can you compute the sum of square roots of the first 86 natural numbers, rounded to the nearest integer? In other words, we are looking for $\sqrt{1} + \sqrt{...
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2answers
158 views

Rectangles and squares of trominoes filling a grid

Let's have a board 24 squares by 24 squares. This board is to be filled with trominoes of three different colors. There are equal numbers of trominoes of each color. The board is to be filled with ...
2
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1answer
125 views

Replacing numbers on a board by their difference [duplicate]

The numbers from 1 to 1000 are written on a board. You are allowed to select any two numbers, erase them and write their difference on the board. If this process is repeated often enough, there is ...
0
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2answers
215 views

Are three colors sufficient to color a map with convex regions?

The four color theorem states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. If all regions are convex (i.e. the region ...
7
votes
1answer
783 views

Cutting off one's nose to spite one's eyes

Disclaimer: to keep graphic depiction of gratuitous violence to a minimum the face to be spited has been deliberately kept abstract. You are required to further reduce any distress this puzzle may ...
3
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1answer
347 views

Using squares to prove e > 2.7

Edited to replace $\exp(-x)$ with $\exp(x)$. My apologies. I loved this puzzle, so thought I'd submit a similar one: The definite integral $\int_{−\infty}^{1} \exp(x)dx$ is equal to $e$ . Using ...
5
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2answers
251 views

Longest sequence of two-digit sum replacements

You are given a two-digit number. You can replace one of its digits with the sum of its digits modulo 10. For example, if the starting number is 58 then you can change it to 38 or 53. You can continue ...
5
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1answer
197 views

Jumping leprechaun on a grid

A jumping leprechaun is a special chess piece that lives on an infinite square grid. On the first turn it moves one cell horizontally (left or right) and two cells vertically (up or down). On the $n$-...
96
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2answers
9k views

Prove that π > 3

It seems that once upon a time some politicians tried to pass a law fixing the value of π to be exactly 3. The idea being to "make math simpler so that our children can get better at math". ...
1
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1answer
196 views

Optimal parking at a concert

You are going to a concert. The road to the concert has 100 car parking spaces arranged in a straight line. The spaces are numbered from 1 to 100, where space 1 is in the beginning of your journey and ...
9
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1answer
1k views

The solution is right in front of your eyes

Although Julius Caesar could not have solved this equation, the solution is related to him: $\quad 63XY-14VZ = 8$ What is the solution?
4
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2answers
221 views

Seven 2s with seven math operations

Linked to A four digit number using exact same 4 digits A number with same repeated digits is called a Repdigit or Monodigit number https://en.wikipedia.org/wiki/Repdigit Can you write an equation for ...
17
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3answers
853 views

Reunite the Stars

On an infinite plane, the Prime Star has disintegrated into four constituent stars, the North Star, the South Star, the East Star and the West Star, each traveling at a constant speed of 1 in their ...
7
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0answers
231 views

A Glutton and a Split Check

N, T, A, B are arbitrary constants in this problem. I have only definitively solved the N=1 subproblem, so, if the general problem cannot be solved, I will be satisfied to mark as accepted a solution ...
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1answer
130 views

Show that every finite directed acyclic graph has at least one source vertex [closed]

Easy puzzle courtesy of a paper I'm reading rn: Show that every finite directed acyclic graph has at least one source vertex. That is, a vertex such that all the directed edges incident to it are ...
4
votes
1answer
198 views

Six single-digit numbers surrounding a three digit number - what's the rule?

Source: SOF World IMO Class 9 Find the missing number, if the same rule is followed in all the three figures. 2 1 4 2 3 3 4 6 7 \ | / \ | / \ | / 693 374 ? / | \ / | \ /...
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2answers
257 views

Five friends and two motorcyclists

Five friends Alice, Bob, Carole, Dylan and Emma are heading to a common destination 100 unit distance away. They start together. Grandma Alice walks at a speed of 1. Bob and Carole walk at speeds 4 ...
18
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4answers
6k views

√2 without pressing √ on a Scientific Calculator

You have to calculate $\sqrt{2}$ on your scientific calculator by only pressing these buttons: ...
3
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1answer
116 views

Exchanging stones on a 8x8 board with sum of two adjacent numbers not being prime

You are given 64 stones labelled with number 1 to 64 each. All those stones are randomly placed on the squares of a 8x8 chess board such that each square is occupied with exactly one stone. A move is ...
8
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1answer
177 views

Going off on multiple tangents

Given two disjoint circles of diameters D1 and D2 draw all shared tangents. Find the intersection points of all pairs of tangents. Discard those collinear with the two circle centre points. Of the ...
8
votes
2answers
497 views

Triangles to diamonds

Given a triangle ABC with sides a=|BC|,b=|CA|,c=|AB| a diamond is circumscribed around the triangle's incircle. The diamond and the triangle share the corner C along with (part of) sides a and b. ...
11
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4answers
788 views

Optimal Path between two concentric circle arcs

When travelling along a outer arc between A and B you have two choices, either diverting onto the inner circular arc or carrying on the outer circular arc, as shown below: You start on the outer arc, ...
3
votes
2answers
137 views

Divisibility by 11 when concatenating the numbers from 1 to 999

As a first step, you write the number 1 on a piece of paper and continue to append step by step the next following integer. After 10 steps the number 12345678910 is written on the paper. How many ...
6
votes
2answers
479 views

The Blindfold CASIO fx-570EX Puzzle

You and your friend are playing a game with the CASIO fx-570EX calculator. The game proceeds as follows: Your friend types a number, then presses a left parenthesis, and then types another number(e.g....
3
votes
3answers
158 views

Rock climbing higher and faster

The Olympic rock climbing competition has 20 climbers. Each climber competes in 3 separate events, where they rank from 1st to 20th. The final score of a climber is the product of their rankings from ...
8
votes
1answer
298 views

Can you distribute the balls equally into 2 boxes?

You have 2 boxes and an even number ($2n$) of balls in the first box. Your goal is to distribute the balls equally into the two boxes, so that each box contains $n$ balls. You must obey the following ...
0
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0answers
79 views

Prisoners splitting Gold [duplicate]

During a mass prison escape, 1000 prisoners managed to break into a prison safe and steal 100 gold bars. Since all prisoners wear shirts with consecutive numbers from #1 to #1000, they decided to ...
5
votes
1answer
115 views

Reconstructing sport climbing results

Sport climbing at the 2020 Summer Olympics – Women's combined Warmup Sport climbing is a new event (one of four) at the 2020 Summer Olympics in Tokyo, and it just finished. Two events were held, one ...
9
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2answers
349 views

Climbing scoring puzzle inspired by today's olympic event

Necessary information. The sport climbing consists of three disciplines: speed climbing, bouldering, and lead climbing. In combined events, the disciplines come in this order, and the combined score ...
8
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4answers
882 views

Not an affix-riddle at all

Slice my neck, that's quite epic. Slice my thigh, that's quite demonic. Slice my waist, you shall have a kill. Slice all three, that's an overkill. What am I? Subtle hint: Moderate hint: Decisive ...
8
votes
1answer
254 views

Existence of index-uniform Hashi puzzles

On the left, we have a starting configuration for a game of Hashi, and on the right, its solution: That is to say, the goal is to make connections (planar, and traveling only in cardinal directions) ...
25
votes
3answers
4k views

Rock climbing at the Tokyo Olympics

The idea for this puzzle came from my friend Jan. The puzzle is based on real world events from the Tokyo Olympics. The Olympic rock climbing preliminary round has 20 climbers. Each climber competes ...
-2
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2answers
139 views

How to solve this problem on overlapping?

In cases of problems involving order and ranking where there are two indices (namely left and right) there is a particular chance of overlapping. Let us take an example to justify this: Ranjan is ...
-6
votes
1answer
152 views

The three door puzzle [closed]

In a long room are three doors. Behind each door one block is hanging from the ceiling. Behind the first door the block is made of concrete; behind the second door the block is made of hardwood; ...
32
votes
7answers
2k views

Two out of a dozen cartons have Easter eggs. Two people try to find one Easter egg carton, each using a different strategy. Who is expected to win?

I have found a counter intuitive puzzle. I have read the answer given at the source and understand it completely. But, what I am unable to understand is why my intuition turned out to be wrong. ...

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