11
votes
0answers
95 views

The Right Triangle Game

I am looking for a deeper understanding, particularly the optimum strategy and the maximum score as a function of grid size, of the following (single-player) game played with an $n$ by $m$ grid: ($6 ...
3
votes
0answers
86 views

Which mathematical game or puzzle did you invent?

A couple of weeks ago, a friend of mine showed me a extension of a game we are all familiar with that he was working on. The game we know is called Tic-Tac-Toe, and he was working on his own version ...
2
votes
2answers
82 views

Winning a restricted game of Nim?

Given the following piles, find the Grundy number of the initial position and make the first move in a winning strategy given that no more than two sticks may be removed from a pile at any time. Pile ...
1
vote
1answer
127 views

You are Johnny Depp 3!

An extension of this question. As @Jared stated in his answer the solution is: we assume that the head pirate chooses between multiple possible proposals that maximize his profit by rewarding ...
6
votes
2answers
298 views

You are Johnny Depp 2!

An extension of this question repeated below. A band of 9 pirates have just finished their latest conquest - looting, killing and sinking a ship. The loot amounts to 1000 gold coins. ...
0
votes
1answer
97 views

How to calculate Team Strength for future prediction?

You are given with $4$ players name, namely Player $A$, Player $B$, Player $C$ and Player $D$. These players are grouped into two teams with two players each. A Game is played between the two team.For ...
6
votes
2answers
219 views

How to solve this puzzle?

There are $N$ consecutive doors. Two players 'B' and 'J' plays a game. Both take turns alternately, and in each turn a player can open any one door. They define a block of 3 consecutive open doors as ...
5
votes
3answers
214 views

How to formally model the “hesitation” in the hat-guessing puzzle?

Hua Luogeng (in Chinese, 华罗庚) took a hat-guessing puzzle as an illustration in a booklet focusing on mathematical induction. The following description is a literal translation from Chinese. ...
0
votes
1answer
327 views

Nim Variant (Restricted removal)

Alice and Bob play the following game : There are $N$ piles of stones with $S_i$ stones in the $i$th pile. Piles are numbered from 1 to $N$. Alice and Bob play alternately, with Alice starting. In a ...
2
votes
1answer
299 views

Nim Variant (reducing by divisors)

Alice and Bob play the following game. They choose a number $N$ to play with. The rules are as follows: Alice plays first, and the two players alternate. In his/her turn, a player can subtract from ...
8
votes
0answers
369 views

Irreversible chess [closed]

Suppose we play a chess-variant, where any finite number of pieces are allowed, and the board is as large as we wish, but only two kings in total. And there is no 50 move-rule, no castling and no ...
4
votes
2answers
243 views

Newspaper competition

A newspaper launches a competition. It said that readers should submit one number between 1 and 1000. A £2000 prize would be awarded to the person that got the closest to 2/3 of the mean of all the ...