All Questions
14
questions
0
votes
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answers
57
views
$m$ players choosing from $n$ integers game
$m$ players play a game in which they pick distinctive integers in the range $0:n$ one after another. Then we pick a random integer from $0:n$. Whoever is closest to our pick wins.
What's the optimal ...
1
vote
0
answers
281
views
Cyclic Partisan Nim Variant
This game is played with a sequence of heaps and a position marker, where each heap is owned by exactly one player. The game ends when a player has removed all objects from their own heaps, and this ...
- 330
2
votes
0
answers
135
views
Clearing all levels with minimum coins [closed]
Thor is playing a game where there are N levels and M types of available weapons. The levels are numbered from 0 to N-1 and the weapons are numbered from 0 to M-1 . He can clear these levels in any ...
- 29
3
votes
2
answers
236
views
What is the minimum number of questions to find the ring
There are 11 rings around a circle numbered from 1 to 11. We know that exactly 9 of them are fake and exactly 2 of them are real rings. In each step, we can choose 5 consecutive rings and ask the ...
- 189
2
votes
1
answer
66
views
Decomposing into sum game
There are $n$ numbers $a_1, a_2, ..., a_n$. Two players take turns. In each move, player chooses some number $a_i$ and writes it as a product of two numbers in any way he wants (so for exapmle $1470 = ...
7
votes
1
answer
830
views
Alice and Bob make all numbers to zero game
Alice and Bob are playing a number game in which they write $N$ positive integers. Then the players take turns, Alice took first turn.
In a turn :
A player selects one of the integers, divides it ...
- 235
1
vote
1
answer
1k
views
Alice and bob xor nim game
Alice and Bob are playing a game. The rules of this game are as follows:
Initially, there are $N$ piles of stones, numbered $1$ through $N$. The i-th pile contains $A[i]$ stones.
The players take ...
- 235
3
votes
1
answer
2k
views
How many pawns, bishops, rooks or kings can be put on a $n \times n$ chessboard such that they don't threaten each other?
A friend of mine asked me this question and I know this is not easy to solve.
I found some informations similar to this question here: https://en.wikipedia.org/wiki/Eight_queens_puzzle;
First of all, ...
- 33
1
vote
0
answers
149
views
Number of ways to make first move
Alice and Bob are playing a game. They have N containers each having one or more chocolates. Containers are numbered from 1 to N, where ith container has A[i] number of chocolates.
The game goes like ...
- 167
3
votes
1
answer
224
views
Play with pairs of numbers
Two players are playing a game. The game is played on a sequence of positive integer pairs. The players make their moves alternatively. During his move the player chooses a pair and decreases the ...
- 1,056
8
votes
3
answers
1k
views
A Nim-like game with conditions and strategies
The game:
Given $S = \{ a_1,..., a_n \}$ of positive integers ($n \ge 2$). The game is played by two people. At each of their turns, the player chooses two different non-zero numbers and subtracts $1$...
- 773
3
votes
2
answers
194
views
Google Question: Number of ways to select sets such that n is pure
Consider a subset $S$ of positive integers.
A number in $S$ is considered pure with respect to $S$ if, starting from it, you can continue taking its rank in $S$, and get a number that is also in $S$, ...
- 315
10
votes
1
answer
433
views
permutation search game
Arrange the natural numbers $1$ through $n$ in a random order (the order is unknown and has a uniform distribution). Now make a sequence of guesses as to which number is in which slot, one number and ...
- 9,927
3
votes
1
answer
122
views
Average result of game
I'm trying to find the average result for a game where you have 12 items (containing a score), you can pick up to five of them, one of them is a multiplier, that when selected multiplies your result ...
- 133