All Questions
51
questions
0
votes
1
answer
84
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Largest collections of subsets [closed]
I need to find largest collection of subsets of $\{1,\ldots, 84\}$ such that each subset has size 5 and any two distinct subsets have exactly one element in common.
Any help is appreciated, Thanks
- 378
3
votes
1
answer
124
views
Given 99 bags of red and blue sweets, is there a selection of 50 bags containing at least half of each type of sweet?
Assume you have 99 bags containing sweets of two kinds, say blue and red.
Is it always possible to pick out 50 bags such that you have at least half the total of red sweets and half the total of blue ...
- 41
1
vote
2
answers
92
views
$2n$ knights around a table with namecards, is it possible that for every rotation there is exactly one person with a correct namecard?
I need help with the following puzzle:
Consider a round table which hosts $2n$ knights. At each seat, there is a namecard of one knight. The knights don't necessarily sit in front of their own ...
- 184
1
vote
0
answers
79
views
Solving formulas for Coupon Collector's problem variant
I considered a modified version of the Coupon Collector's problem where there are $m$ transparent balls, $k$ different colors and $c$ balls of each color for a total of $n=ck+m$ balls in the urn.
I ...
- 31
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
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
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, ...
10
votes
3
answers
284
views
How would you go about learning the combination of coins the man has?
I am trying to identify the branch of math that would help to solve the following problem:
A man has picked $10$ coins out of a bag and has laid them in a row. You cannot see them for yourself, and ...
- 103
1
vote
1
answer
72
views
Construction of a vector consisting of entries with a peculiar pattern
Note: A similar problem was asked in this MO post, but no importance was attached to order of nonzero numbers and zeros
Consider constructing a $n$-tuple of numbers $v=(a_1,a_2,\ldots,a_n)$ consisting ...
- 7,085
1
vote
1
answer
204
views
Counting how many items can be weight on a scale if we pick the weights optimally [duplicate]
I am reading about a problem that states the following:
Suppose you have a balance and are allowed to choose the weights for
its functionality. The objective is to pick the weights in a way that
...
- 1,609
1
vote
0
answers
94
views
The first thought for this puzzle is wrong but it is also one that seems most natural. What is the correct comparable approach?
There is the puzzle that given the information that:
a clock at 6 o'clock struck 6 times and the time elapsed between the
first and last strike was 30 seconds asks how long will it take to
strike 12 ...
- 1,609
1
vote
2
answers
145
views
Couple problems and classic wolf/goat/cabbage and abstraction
I was reviewing Dijkstra's approach on the problem/puzzle of how 2 married couple can cross a river with 1 boat that can carry 2 people. The original problem's restriction is that the wife can't be in ...
- 1,609
0
votes
1
answer
334
views
Covering an 8x8 board with L and O Tetromino [duplicate]
I solved a puzzle about proving that if a rectangular board can be covered by L-Tetrominoes then the number of squares must be a multiple of 8.
I based the solution on a colored board (like a ...
- 1,609
0
votes
1
answer
222
views
Covering a rectangular board with Tetrominoes
I am reading about a puzzle question that is about Tetrominoes and proving that if a rectangular board can be covered with T-Tetrominoes the board's number of squares has to be a multiple of 8.
The ...
- 1,609
1
vote
0
answers
75
views
$k$ isolated prisoners with hats, $n$ possible hat colors, $k$ tries to guess everyone's color after initial chat before hat assignment
Basic problem:
$2$ prisoners are in a room, they are allowed to chat and come up with a plan for the riddle they are about to face. After their chat, they are separated and assigned one hat each, ...
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