All Questions
16
questions
3
votes
0
answers
80
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
126
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. ...
- 21
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 ...
- 51
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
66
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 ...
- 351
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
827
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
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 ...
- 475
-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 ...
- 167
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 ...
- 311
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 ...
- 11
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 ...
- 1,056
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
1
vote
2
answers
201
views
Some Questions About Chess
I have to questions about the chess game: please help me to understand it.
1- How can a computer program know if this move or that move is better? It calculates all possbile continuation and examine? ...
- 22.6k