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A puzzle that asks for determining the winner in a multi-player game.

59
votes
5answers
Abraham Van Helsing and Jonathan Harker play a game against Count Dracula. … If Jonathan Harker finds the locket with number $N$ during his 500 search steps, then he and Van Helsing have won the game. …
asked Oct 13 '15 by Gamow
13
votes
2answers
The game ends once all squares have been filled. … When the game has ended, Mary receives $N(M)-N(U)$ Euros from Ursula. Question: How much money will Mary receive from (respectively, lose to) Ursula? …
asked Feb 26 '15 by Gamow
13
votes
3answers
A spider and a fly play a game with a cube of side length $s=1$ and with a positive real number $d$. First, the spider picks its starting point $S$ somewhere on the surface of the cube. … The spider wins the game, if it manages to reach the point $F$. Otherwise the fly wins the game. Question: For which values of $d$ does the spider have a winning strategy? …
asked Jan 11 '19 by Gamow
10
votes
4answers
Alice, Bob and Carol sit around a round table. Initially Alice has $n$ cookies, while Bob and Carol have none. Alice divides her cookies evenly between Bob and Carol; if there is a leftover cookie (as …
asked Sep 13 '15 by Gamow
23
votes
2answers
The first player who cannot move loses the game. Determine the winner of the game for every combination $(m,n)$ of positive integers $m$ and $n$. …
asked Jan 23 '15 by Gamow
14
votes
2answers
Alice and Bob play the following game with $n\ge2016$ chips on the table. Alice and Bob move alternatingly. Alice makes the first move. … The player who takes the last chip wins the game. Question: Which player is going to win this game? (As usual, we assume that Alice and Bob both use optimal strategies.) …
asked Jan 10 '16 by Gamow
14
votes
3answers
The game then goes on with the remaining coins. Cosmo may end the game after any round, by pointing at two coins still on the table and announcing that their total value is at least $28$ Euro. … Cosmo wins the game if and only if his announcement is correct. Question: How can Cosmo enforce a win? …
asked Dec 23 '15 by Gamow
32
votes
4answers
Finally they decide to play the following game. In every step, Stanlio picks a handful of gold coins from the loot. Then Ollio decides, whether this handful should go to himself or to Stanlio. … Once all coins have been assigned, the game ends. Once one of them has received 9 handfuls, the game also ends. …
asked Feb 20 '15 by Gamow
49
votes
4answers
The lion plays a deadly game against a group of 100 zebras that takes place in the steppe (= an infinite plane). … The lion wins the game as soon as he manages to catch one of the zebras. Will the lion always win the game after a finite number of moves? …
asked Feb 16 '15 by Gamow
18
votes
6answers
Alice and Bob play the following number guessing game. In the beginning, Alice picks a secret number from the range $1,2,3,\ldots,144$. Then Bob is allowed to ask a sequence of questions. … The game ends, once Bob chooses a one-element subset to which Alice answers YES. Bob then receives $x$ Euro from Alice. How should the value $x$ be chosen, so that these rules do yield a fair game? …
asked Feb 12 '15 by Gamow
6
votes
2answers
Alice and Bob play a game by alternately placing dominoes on a $3\times100$ checkerboard (3 rows, 100 columns). Alice has the first move. … Determine the winner of the game. (As usual, we assume that Alice and Bob use optimal strategies.) …
asked Feb 7 '15 by Gamow
14
votes
1answer
If Cosmo can form such a triangle: Cosmo has won the game. … Will Cosmo always win the game after a finite number of steps? For any choice of wooden sticks to start with? …
asked Feb 5 '15 by Gamow
7
votes
2answers
Professor Egghead participates today in a local game show. … According to the rules of the game show, Egghead announces three guesses for each of the jewels: I guess that the diamond is in one of the three boxes D1, D2, D3. …
asked Feb 22 '15 by Gamow
38
votes
6answers
Alice and Bob play a game that starts by Bob picking a secret integer $N\ge100$. Then the game goes through several rounds. In every round, Alice picks an integer $x\ge3$. … If $x$ divides Bob's current secret value $N$, then Alice wins and the game ends. …
asked Mar 10 '15 by Gamow
14
votes
4answers
Determine the winner of the game. (As usual, we assume that Alice and Bob use optimal strategies.) …
asked Jan 29 '15 by Gamow

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