Tessellate S.T.E.M.S - Computer Science - College - Set 2 - Subjective Problem

There were three brothers: Ignotus, Antioch and Cadmus.

They are playing a game with $n$ pebbles, where the brothers take turns. Ignotus goes first followed by Antioch and then by Cadmus and this game goes on. During each turn, each of the brother removes either 1, 2 or 3 pebbles from the pile. The winner is one who takes the last pebble from the pile.

However, Ignotus knows that Cadmus will never draw the same number of pebbles from the pile as Antioch did in during his turn in the same round.

With this knowledge, for what values of $n$ can Ignotus win the game?

This problem is a part of Tessellate S.T.E.M.S.

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Comments

The goal seems to be to leave the other brothers with 6. Then (since they can't take 3+3, or 1+1) whatever they take, Ignotus can take the last pebble.

With 6 being a goal, leaving the other brothers with 12 gets you to 6 by the same strategy. Extrapolating, leaving them with any multiple of 6 is a winning play.

Therefore, winning values of n for Ignotus are whole numbers of the form 6m+1, 6m+2, and 6m+3.

Steven Perkins - 3 years, 5 months ago

Nice solution. A very similar generalization of this game is called the Nim

Agnishom Chattopadhyay - 3 years, 4 months ago

I was familiar with Nim as a two person game. This three person variant was interesting.

Steven Perkins - 3 years, 4 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$