All Questions
16
questions
3
votes
0
answers
82
views
A strategy for number-guessing game
Let player A and player B are playing number-guessing game, which is:
Player A draws one natural number $X$ in $1,2,\cdots,N$ at random.
Player B guesses a number $Y$ in $1,2,\cdots, N$.
Player A ...
- 918
2
votes
1
answer
132
views
Optimal strategy in number guessing game?
Consider the following game.
Two players each create a passcode using the digits 0-9 four times with repetition allowed.
The two take turns asking a yes or no question about the opponent's passcode. ...
- 82.2k
1
vote
0
answers
95
views
Building a primitive programming language for solving math olympiad problem(TSTST 2015)
There was a 6th problem on USA TSTST 2015:
A Nim-style game is defined as follows. Two positive integers $k$ and
$n$ are specified, along with a finite set $S$ of $k$-tuples of
integers (not ...
- 61
0
votes
0
answers
147
views
Guessing a secret number to maximize the result
You are given a set $A$ (all elements are different and positive) and
a set $B$ (all elements are different and positive).
Find a optimal number $x$ ( $0 < x \leqslant W$ where $W$ is a given ...
- 195
0
votes
1
answer
67
views
Find the longest subinterval of [0,1] with a finite number of queries
We have a number of intervals (either finite or infinite), not overlapping if not for their extreme points, which union is [0,1]. One of them is long at least 1/4, and all the others are not longer ...
- 11
1
vote
1
answer
63
views
Binary search on positive integer valued random variable
Let $X$ be a random variable taking values in $\{1,2,3,...\}$ and $\mathbb{E}(X)<+\infty$. $A$ has a realization of $X$. $B$ wants to guess what value does $A$ have and $B$ knows the distribution ...
- 239k
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 ...
- 24.5k
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 = ...
- 378k
4
votes
1
answer
679
views
Knight movement on chess field
I had this task in programming competition: There are two knights, which are $(p_1,q_1)$ and $(p_2, q_2)$. $(p,q)$ knight is figure, with p(q)-length first step, and q(p)-length second step in ...
- 378k
-1
votes
1
answer
373
views
Finding winner of flipping game
Alice and Bob play a game with N non-negative integers.
Players take successive turns, and in each turn, they are allowed to flip active bits from any of the integers in the list.
That is, they ...
- 378k
0
votes
1
answer
2k
views
Number of ways to win chocolate game
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 ...
- 40.9k
1
vote
2
answers
739
views
Game of cards and GCD
Alice and Bob play the game. The rules are as follows:
Initially, there are n cards on the table, each card has a positive integer written on it.
At the beginning Alice writes down the number 0 on ...
- 2,605
1
vote
1
answer
220
views
Game Of Strings
There are two strings A and B. Initially, some strings A’ and B’ are written on the sheet of paper. A’ is always a substring of A and B’ is always a substring of B. A move consists of appending a ...
- 10.4k
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 ...
- 378k
38
votes
1
answer
3k
views
Is War necessarily finite?
War is an cardgame played by children and drunk college students which involves no strategic choices on either side. The outcome is determined by the dealing of the cards. These are the rules.
A ...
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