Ariadne's String

Two threads cross one hall, each step longer than that thread’s last, and the first with no longer step left loses.

The Ariadne's String board

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Grades
4–6
Subjects
Shapes & Space, Logic
Kind
Two-player game
Cost
Free, no account, no ads
Original
Ariadne’s String Game at MathPickle

What it is

Two players, the Minotaur and Theseus, each lay a thread across a hall of pillars. The first tap sets your spool down; after that each tap walks your thread to a pillar, and every step has to be longer than your own last one. No thread may touch the other, or itself, not even at a single point. Whoever cannot take a longer step loses.

The rules

Two players walk two threads through a hall of pillars: the Minotaur's and Theseus's.

An empty hall of pillars. A tap sets the Minotaur's spool down near one wall, and that pillar becomes a hole. Theseus taps the pillar straight opposite it, through the middle of the room; the board says no with a red line from one to the other through the middle. Theseus taps somewhere else and the spool goes down.
Your first tap sets your spool down, and that pillar becomes a hole. Not on the other spool, and not straight opposite it through the middle of the room.
The Minotaur's thread has taken a step of one pillar and then a step of root five. A tap two pillars straight up is refused: a red circle the size of the last step appears round the head of the thread, and the tapped pillar is inside it. A tap 3 across and 2 up is taken instead, and its sum is written on it: 3 squared plus 2 squared is 13, a step of root thirteen.√532√13
Then tap a pillar to step there. Every step must be longer than your last one: nothing inside the red circle will do. 3 across and 2 up is 3² + 2² = 13, a step of √13.
Theseus taps a pillar on the far side of the Minotaur's thread. The step would cross it, so the board says no by lighting the stretch of thread in the way in red. Theseus taps a pillar on his own side instead, and his thread steps there, clear of the other one.
Threads must never touch: not the other one, not your own, not even at a single point.
The Minotaur's thread walks to a corner and then takes the diagonal of the whole hall, the longest step there is. Theseus takes two short steps. Then it is the Minotaur's turn, and nothing beats its last step: a red circle the size of that step appears round its head, wider than the floor, with no pillar outside it.√32
Take a giant step and you may have nothing longer left. The first player who cannot step loses.

What it gives you to practise

Comparing lengths by squaring. A step three across and two up is √13, because 3² + 2² = 13, and the line over the board says that sum on every turn, so whether the next step beats it is a question about whole numbers. Then the game: a long step now is a long one to beat later, and every step laid is a wall the other thread has to walk round. Help draws the circle each thread has to land outside, and the pillars it can still reach.

In a classroom

Gordon Hamilton’s paper game, from MathPickle, where he suggests a 5 × 5 for one against one. Here it is played against three rivals, one pack each and named for what they do — one takes the biggest stride, one saves every step it can, one counts the steps both of you have left — in halls of 5 × 5, 6 × 6 and 7 × 7. Two Spools is the same three halls for two people on one tablet, measured even for both, and they play over an online room too. One rule is added to Gordon’s: a spool may not go down straight opposite the other one, because from there the second player could copy every step through the middle of the room — the symmetric reply Gordon himself points to on the even boards. The board prints as an empty hall of dots, for two pencils.

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The whole game at one address, with every board in it. Whoever opens it stays inside it, and their progress stays in their own browser.

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