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I think they can, in theory, In the following way. Second generation Now we have a second generation consisting of Third generation Now we have a third generation consisting of Four …

After 40 moves by each player, 150 minutes have elapsed on each player's clock. So the average time taken for a move is exactly $150/40=3.75$ minutes, i.e. 3 minutes and 45 seconds. Question 1 The a …

Let's call someone a Halfer if they have a €0.50 coin and a Wholer if they have a €1.00 coin. The problem is essentially to find the number of possible queues such that since the machine takes a €0 …

Let $B_1,B_2,\dots,B_{99}$ be the bags, in increasing order of number of apples contained; say the number of apples in $B_i$ is $a_i$ for all $i$. If our 50 bags grabbed are $B_{99}$, one of $B_{98}$ …

The puzzle is Proof Split the infinite grid up into NW-SE diagonals of length 1, 2, 3, 4, ... Assign each cell a value Then the total value of all occupied cells is an invariant, because each …

The answer is the proof being as follows. (Thanks to @El-Guest for finding the error in my previous reasoning!) This assumes that rotations and reflections of the same path count as different fr …

Yes: the solution was already mentioned in this answer, sourced to this page.

First observation: the colour of the knights corresponds to the colour of the squares - the black knights must be all on one colour and the white knights all on the other colour, since a knight's move …

Here's the solution: It's interesting to note that the domination problem has very few solutions for 3 queens on a 6x6 chessboard as compared to other possibilities. (Neither of those links contain …

Solution to the question as stated It can be done in 92 moves. Here's how (using standard chessboard notation, rows numbered from a to g and columns from 1 to 7): move the white pawn on a1 to a5 (4 …

Inspired by my answer to a more general puzzle. This is a stream-of-consciousness answer showing exactly the thought process needed to find the solution. If you just want to know the answer, skip to …

It's possible if and only if Proof is as follows. $n\leq3$ $n>3$ For example, with $n=7$ we have

Partial answer Unless my physics is wrong, the fact that the pans have different weights and the arms have different lengths means that there exist constants $a$ and $b$ such that the two pans balanc …

Fix $K$. We will find conditions on $i$ for the road sign numbered $i$ to be as desired. Write $i$ as a $K$-digit number, say $i=i_1i_2i_3\dots i_K$ where each $i_k$ may be any digit from zero to nin …

$n$ even A solution is possible for Proof is as follows. $n$ odd A solution is possible for Proof is as follows. How did I find this? (SPOILERS) Well, let's start with $n=5$. Now we kno …