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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10000 rounded to the nearest integer is 22
10000 rounded to the nearest integer is 22,
20000 rounded to the nearest integer is 2101,
100000 rounded to the nearest integer is 212, and
200000 rounded to the nearest integer is 21010.
What is ...
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2048: how many sets of moves have I made? [duplicate]
Transcription of board (score 324):
2
2
32
4
8
16
2
32
4
4
8
2
I made moves in the pattern of: right up left down right up left down. How many times have I done this set? (1 set=right up left ...
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5x5 grid with a special colouring
Can you paint the cells of a 5x5 grid in 5 colours such that for each cell its colour and the colour of its orthogonal (horizontal and vertical) neighbours are all different?
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2048: How many turns did I survive?
Here's my most recent 2048 game:
Clicking on the image takes you to the 2048 site.
Transcription of board (final score 59612):
2
4
8
4
8
32
64
16
4096
2
512
256
2
8
1024
8
How many turns ...
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How many dogs of Oxford are there?
The dogs of Oxford, I declare:
Numbered one third of a square.
If one quarter left to roam,
Just a cube would stay at home.
What is the smallest possible number of dogs in Oxford?
This is a ...
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Longest Fibonacci word
Fibonacci words are defined as $F_0 = a, F_1 = b, F_{n+2} = F_nF_{n+1}$ where $a, b$ are letters. How can you find the longest Fibonacci sub-word in a given string?
Try to solve it in linear time ($O(...
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Using 8 6 4 2 = 6 in that order using only x - +
One more question..
Using 8 6 4 2 = 6 in that order using only x - + 👍🏾
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3
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The infinite bag of billiards balls
The following trio of puzzles comes from http://skepticsplay.blogspot.com/
My question is: What is the solution to variation 2?
The original author of these puzzles described them as being abstract. ...
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Let's make a huge number with only tiny numbers (pt3)
Previous huge out of tiny puzzle by TerriblyDrawn
Using only four ones, four twos, and five fives (1, 1, 1, 1, 2, 2, 2, 2, 5, 5, 5, 5, 5), can you make the complex number$$51+5i\sqrt5$$You can use ...
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Let’s make a huge number with only tiny numbers (pt2)
Using only three 1s and two 2s (i.e. 1,1,1,2,2), can you generate the smallest 3-digit prime number, 101? You can use all mathematical operators you know, such as floor function, factorial, powers/...
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Let's make a huge number with only tiny numbers
Using only three 1s and two 2s (i.e. 1,1,1,2,2), can you generate the number 55? You can use all mathematical operators you know, such as floor function, factorial, powers/indices*, etc., but ...
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Seat criminals around a circular table so they are not close to enemy
This puzzle is an 7-9 grade math Olympiad puzzle.
50 criminals came to a meeting. Each of the criminals has a maximum of 24 enemies among those who came to the encounter. Prove that it is possible to ...
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Primeable numbers
Say a positive integer is primeable if it is prime or some permutation of all its digits (leading 0s allowed in permutations) is a prime. Thus the first few primeable numbers are 2, 3, 5, 7, 11, 13, ...
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this puzzle is based
This message is a basic numeric substitution cipher. The key is the standard, regular alphabet in the correct order (ABC...XYZ).
Here is the message:
3 16 15 7 20 1 22 23 13 1 22 10 16 15 21 27 16 23 ...
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Shiny cryptarithm
Here's a little puzzle I made today:
$$\sqrt{\text{ILLUMINATE}^{\mathstrut}} = \text{LIGHT}$$
Most usual rules of alphametic puzzles apply here: the same letter always represents the same digit, and ...
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How to remember without writing, a subset of 1000 numbers [closed]
P has a secret number which is between 1 and 1000 (both inclusive).
Q tries to guess the number by speaking out random numbers one by one.
R has to keep track of all the numbers that Q has spoken. An ...
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votes
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1000 Batches, 1 Poisoned, 4 Mice, Minimized Costs
You work at a pill factory that recently produced $1000$ batches, each with ample samples. Your boss has just discovered that exactly one batch is entirely poisoned, and just one pill from it will ...
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What is the probability I can't bike despite good weather? [closed]
I am trying to solve this puzzle:
I have a total of two bikes that I keep at work or at home. I always bike to and from my work unless it rains, in which case I take a taxi (and don't bring my bike). ...
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Find all the real money
An eccentric billionaire invites you to join in one of her strange games. She lays before you 1000 $100 notes, and announces that half of them are actually fake. You check the notes carefully, finding ...
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Show that 29 divides 3a+2b if and only if it divides 11a+17b [closed]
Let a and b be integers. Show that 29 divides 3a+2b if and only if it divides 11a+17b.
I am unable to solve this
Am I correct in interpreting this as : "If 3a+2b is divisible by 29 then prove ...
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An optimal puzzle (unit)
Given the image below, which of the options, A-E, should replace the question mark? Explain your reasoning.
Hint 1
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Numbers that are averages of their digits
A number is called special if its decimal value^ is the average of its digits. How many special numbers are there? Bonus: How many special numbers do not begin with the digit 0? Good luck!
^ You are ...
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votes
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Reducing π to zero (again)
You are given the first 20 digits of π: 31415926535897932384. In each move, you can select a contiguous group of 5 digits and increase/decrease them all by the same integer, provided that each ...
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frog on a number line
A Frog is at C. The purple numbers are the probability that the frog jumps in that direction when it is at certain place. The frog stops at A or E. What is the probability that the frog stops at A?
...
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Interesting irrational number
Can you find an irrational number $x$ such that $x$, $1/x$ and $x^2$ all have exactly the same digits after the decimal point? Good luck!
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Logic and Geometry Problem #5: does Savage Go have cycles?
My question is whether or not a cycle can occur in the game of Savage Go. That is, you kill some of mine, I kill some of yours, you kill some of mine... Endless cycle of turns. Game never finishes.
No ...
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How many 4x4 Latin Squares are there?
I thought of this problem when playing Sudoku. Let A = {1,2,3,4}. I have to make a 4x4 box (i.e. the size of A in both dimensions) and fill it with data such that ...
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Don't let 'em die!
There is an 8x8 array of sleeping humans with ten feet between adjacent humans, with sides in the four cardinal directions. A hero and a villain start ten feet west of the northwest human. The hero ...
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Waffleing my Egg
This morning I had a waffle and a fried egg for breakfast. The fried egg was cooked with a mold, so it was perfectly round and three inches in diameter. The waffle was a 3-inch by 4-inch grid of one ...
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Can you find a 3x3 white square somewhere in this relatively prime graph?
This puzzle comes from: http://skepticsplay.blogspot.com/search/label/puzzles
Wow, it's been some time since I've posted a puzzle! Here's a simple pure math puzzle off the top of my head.
Back in ...
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Permutations with given longest increasing subsequence
How many permutations of 1 to 20 are there with 2,5,6,9,13
as a longest increasing subsequence? (It may be tied with others.)
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Minimum K for detecting fake pearls in one weighing
There are 10 boxes, each with the same number of pearls (represented by K). Genuine pearls weigh 30g each, while fake pearls weigh 29g each. Each box is either all genuine or all fake, and any number ...
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Can you find the missing letters?
A pattern of letters has had letters 10 through 20 deleted. Your job is to find out what letters should go in spots 10-20. Here is the pattern:
a, b, c, d, d, d, f, e, f, _, _, _, _, _, _, _, _, _, _, ...
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Cutting the points evenly
I draw an even number of points on a piece of paper. Is it possible to cut the paper into two pieces with a single straight cut, such that:
Each piece gets the same number of points
The cut does not ...
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Puzzling Pelican Pebbles
Story Setup
It's Percy the Pelican's first day running the front desk of his master's magical pebble shop. His job is to fetch pebbles from the stock room to fulfill customer orders.
The stock room ...
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#TenderfootSpiral
Clues:
Two hikers on an incline arrow with numbers.
Hiker 1 says: 38.548493. Hiker 2 says: -105.998749.
Sequence: Hiker 17711 Hiker 0 377 0 144 1 10946 233 987 0 2584 6765 75025
Hiker = ...
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Intermingled primes
This puzzle is part of the Monthly Topic Challenge #14: Think inside the (very small) box!.
6 different, 3 digit primes are stacked here in two layers.
You only see the sum of overlapping digits.
...
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Another paint balls problem [closed]
Suppose you have 2n balls with 1 of them being red and the rest being white. In each round the balls are randomly paired into n pairs. All white balls in a red-white pair are painted red. What is the ...
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Closed path on a dodecahedron
Your task is to draw lines between edges on a regular pentagon such that if you tile a dodecahedron with 12 identical copies of that pentagon you get a single closed line which does not intersect ...
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Expected number of steps [closed]
There are N cars that are parked in N parking spots numbered from 1 to N. After the Nth parking spot, there are N more parking spots numbered from N+1 to 2N. At each step, a car is selected randomly ...
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The Triangular Cannonball Problem [closed]
How many ways are there to stack an equilateral triangle of cannonballs into a tetrahedron of cannonballs? In other words, how many positive integers are both triangular and tetrahedral?
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A colorful dodecahedron
Divide a "base" edge of a regular pentagon into three equal parts. Then draw two lines from the base to the center of the other edges such that the lines do not intersect. This splits the ...
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Is this duplo train track under too much tension?
My kids were making this train track of duplo the other day, and this is what they put together. They are still very young, and for them, this is something big. They were really proud that they ...
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Figure Out The Language: Min
Imagine there is a programming language in which you can only evaluate expressions. Expressions have operators and constants.
There are three types of constants.
Numbers - Any number from 0 to ...
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Connect dots on a grid with one continuous line (optimization)
(This question is the third puzzle of the Connect dots puzzle series. You can find the first two puzzles here and here, respectively.
The original question and photos originate from webadventurer. ...
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Find unique values for the variables to make all statements true
In this puzzle you have to find unique values for the variables to make all statements true. I have proceeded to here and now I seem to be stuck.
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Logic and geometry problem #4: are these games functionality equivalent?
Two games, Crossway and Mincut, are believed to be functionally equivalent. That is, a win by Crossway rules will necessarily lead to a win by Mincut rules. And a win in Mincut will be a win in ...
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Regular polygons meeting at a point
How many ways can regular (convex) polygons meet at a point (vertex), so there are no gaps or overlaps?
Here's an example with a square, hexagon, and dodecagon.
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