All Questions
88
questions
4
votes
1
answer
146
views
Formalising the problem and create a proof for the game "Waffle"
Waffle is an online game at https://wafflegame.net/daily.
It consists in moving letters (swapping them) to recreate the original words. While you have 15 moves, it can be done in 10. I usually try to ...
- 1,125
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
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
4
votes
0
answers
109
views
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
views
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
3
votes
2
answers
669
views
Coin weighing puzzle
I have 4000 coins, 2000 coins weighing 1 gram and 2000 coins weighing 2 grams. I cannot tell the difference between these coins. However, I have a weighing scale (like a digital one, not a balance ...
- 31
2
votes
0
answers
152
views
$8$-coin problem with $3$ balance scales ($1$ broken) and its generalization
You've $8$ identical-looking coins. All the coins weigh the same but $1$ coin is lighter than the rest. You're given $3$ double-pan balance scales. $2$ of the scales work, but the $3$rd is broken and ...
0
votes
1
answer
69
views
Puzzle: Calculate amount of combinations of "houses" [closed]
I've found this enigma in a french book and I've tried using combinatorics to find the answer but I've been unsuccessful, could you help me out?
Here's what's given:
"A child wants to build "...
5
votes
2
answers
203
views
Edgematching tiles
Consider a 3×3 grid. Now, look at the patterns which generate 1 to 7 dots around the edges, taking into account rotations and reflections. Turns out there are 49 patterns, as seen in the set below ...
- 21.4k
9
votes
3
answers
696
views
Difference Triangles
In a difference triangle, a row of $n$ integers is given, then their differences are written underneath, and then another row of difference is added, until there is a triangle of $n (n+1)/2$ integers. ...
- 21.4k
6
votes
2
answers
851
views
Towers of Hanoi if big disks can go on top of small disks
The Tower of Hanoi puzzle is concerned with moving $n$ disks between three pegs so that a larger disk cannot be placed on top of a smaller disk. Based on a (now deleted) StackOverflow question, ...
4
votes
1
answer
209
views
Coin weighing puzzle: one heavy coin, one light coin, which together weigh the same as two normal coins
My question was inspired by this previous question.
There are $c = 3^k$ coins where $k \ge 2$. Among these coins:
$c-2$ of them are good and weigh the same.
The remaining $2$ coins are bad: one of ...
- 15.5k