All Questions
Tagged with combinatorics recreational-mathematics
628
questions
1
vote
1
answer
210
views
The toys problem: Probability of getting two matching good item and a different third Item
I've encountered an intriguing probability problem. I just registered to ask this, so this will be my first post.
Disclaimer: I met this problem in a real setting that's it too convoluted to explain (...
- 13
6
votes
1
answer
438
views
Placing the $21$ two-digit primes into a grid, such that primes in adjacent squares have either the same tens digit or ones digit
This is USAMTS round 3, problem 1 of the 2020-2021 Academic Year.
Place the 21 2-digit prime numbers in the white squares of the grid on the right so that each two-digit prime is used exactly once. ...
- 1,837
6
votes
1
answer
335
views
Minimum swaps to put an array into desired order, where some elements are identical/repeated
Inspired by a word game Waffle, see footnotes if interested. The abstracted problem:
You're given an input array of letters, some of which might be identical (i.e. repeated), e.g. ...
- 15.5k
3
votes
1
answer
83
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Find max N people with 2022 different colored balls choosing two balls each so that no 3 people exactly contain balls of 3 colours
Here is the "exact" wording given in the problem.
There are $N$ people. Each person gets two balls of different colours among $2022$ balls with different colours. The combinations of the ...
- 125
0
votes
1
answer
101
views
A dice with numbers 1 to 10 is thrown 4 times. Find the probability that result has 3 consecutive prime or no prime shows up three times consecutively
Here is the exact wording in the problem given.
Numbers from 1 to 10 are printed on a fair 10-faced dice. The dice is thrown 4 times.
Find the probability the result has 3 consecutive prime numbers or ...
- 125
0
votes
0
answers
44
views
Number of possible solutions given a specific input
Given a set of positive integers $N_1,N_2,...N_N$ and a function $f(x)$ where $f(x)=ℤ$ for all $x \in ℤ$.
There exist solutions of the form $n_1,n_2,...n_N$ where $n_i \ge 1$ and $n_i \in ℤ$ subject ...
- 1
2
votes
1
answer
102
views
Find the number of subsets of n chairs in a circle containing at least three adjacent chairs
Find the number of subsets of $n$ chairs in a circle containing at least three adjacent chairs.
I know that the answer for $n=10$ is $581$, and the solution is here for instance.
I'm not sure if it's ...
- 469
1
vote
1
answer
73
views
How many good distributions of coins are there?
At each vertex in figure 1, there is a student. A total of n = 60k coins are distributed to these students. The coins are redistributed as follows: Each student simultaneously give an equal number of ...
- 469
3
votes
3
answers
349
views
How to think and deduce optimal strategy move for both Alice and Bob
Question:
Alice and Bob are playing a game on a one-dimensional number line. Initially, Alice is standing at coordinate $x=a$ (integer) and Bob is standing at $x=b$ (integer) .It is guaranteed that $...
- 55
7
votes
1
answer
170
views
Maximum possible number of 1012-element subsets of {1,2,...,2024} such that no three intersect at more than one element
I came across the following problem:
At most how many $1012$-element subsets of $\lbrace 1,2,\dots,2024 \rbrace$ may be chosen such that the intersection of any three subsets has at most one element?
...
- 155
3
votes
3
answers
121
views
Coloring the faces of n^3 unit cubes s.t., for each color j between 1 and n, the cubes can be arranged to form nxnxn cube with j-colored outer faces
I encountered the following problem in Paul Zeitz's The Art and Craft of Problem Solving (problem 2.4.16 on page 56 of third edition):
Is it possible to color the faces of 27 identical $1 \times 1 \...
- 155
1
vote
1
answer
96
views
A Bowling Sequence: a(n) returns the number of possibilities for the number of pins knocked down to reach that score.
Once again, my lack of coding ability prevents me from quickly answering a math question that interests me currently. I imagine one of you wizards can knock this out quickly using brute force.
I am ...
- 53
0
votes
0
answers
87
views
3 points blue, red, green form a triangle $T$ in $\mathbb R^2$. 3 points B, R, G inside that triangle. Do all proper rainbow triangles cover $T$?
Suppose I have 3 points colored blue, red, and green resp. forming a triangle $T$ in $\mathbb R^2$. Suppose I have 3 more points colored blue, red, green resp. (possibly overlapping) in the interior ...
- 8,945
4
votes
0
answers
109
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What percent of lighted grids are walkable: a trick-or-treating problem
I am a math teacher that likes to invent fun math problems to explore. Here is one I have been investigating for a little while and have made little progress on because the number of possible $n \...
- 53
4
votes
1
answer
127
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Word and number ladder puzzles
Introduction
$
\begin{array}{}
\begin{array}{c|c|c}
\text{1} & \text{SIZE}\\
\hline
2 & \\
3 & \\
4 & \\
5 & \\
\hline
6 & \text{RANK}
\end{array}
&
\begin{array}{c|c|...
- 3,075