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Results tagged with mathematics
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user 73
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.
5
votes
When can one construct expression dividable by M from any N numbers?
You can always do it if $N \ge M$. Reduce all the numbers $\pmod M$. If any are zero, put multiply signs everywhere. If not, imagine putting plus signs everywhere and keeping track of the running s …
- 9,084
1
vote
A Martin Gardner problem about constructing a scoreboard given minimal information
$40$ total points were scored. As the bottom two schools get at least $3$ points per event and $B$ won one, there were at most $5$ events. So far, we could have $5$ events with a total score of $8$ …
- 9,084
4
votes
Accepted
I Eight Two Much
I take three eights as twenty-four, and can do $(2+2)(2+2+2)$ to get there with five twos. One or two of the plus signs can become multiplies. There are other solutions, depending on what operations …
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4
votes
7
votes
Happy 2023 to all
All numbers greater than some threshold are
To make a bound on the threshold
- 9,084
3
votes
13
votes
Variation of 100 prisoners light problem
If you accept a probabilistic argument, they can get out (or die) much sooner. After $d$ days, the chance that a given prisoner has seen the room is $1-\left(\frac {99}{100}\right)^d$. It is not fai …
- 9,084
7
votes
Accepted
What is the expected length of the longest piece?
This is known as the broken stick rule. The Wolfram Demonstrations Project claims that
If the unit interval is divided into $n $ spaces by $ n-1$ random points, the expected size of the $i^{\text …
- 9,084
22
votes
Accepted
N pirates steal their share of bananas to the benefit of a monkey
The basic idea is to work backwards.
A cute trick is to recognize that there could have been
- 9,084
4
votes
Help understanding the solution to a "shooting puzzle"
The answer does not appear to apply to the question as stated. In the question it says that Jones shoots first, Brown next, and Smith last. The calculation of the chance that it is Smith that Jones …
- 9,084
11
votes
Accepted
Unknown Consecutive Integers Puzzle
From 1 we know that Anne does not have 1. From 2 we know that Bob does not have 1 or 2. From 3, we know that Anne has 3 and knows Bob has 4.
- 9,084
3
votes
How to choose at least half of everything
I think you have alluded to the most challenging distribution. The chests are divided into $G$ chests containing one (or the same number) of gold coins, $S$ containing one silver coin, and $C$ contai …
- 9,084
0
votes
How many balls can fit in the box?
We will assume that we want to find the largest number of balls that can fit in the box when they are hexagonal close packed. The other answers have ignored the edge effects, using the density of ba …
- 9,084
9
votes
Ant walking on a number line
The simple approach is to see it as a coin flipping game where one player starts with $3$, the other with $7$, and the winner of each flip collects $1$ from the loser. As each flip is fair, the game …
- 9,084
8
votes