Minotaur

Every step of the string has to be longer than the one before, and it may never touch itself: how many steps can the way to the Minotaur take?

The Minotaur board

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Grades
4–6
Subjects
Shapes & Space, Logic
Kind
Puzzle
Cost
Free, no account, no ads
Original
Minotaur Gores Pythagoras at MathPickle

What it is

A room of dots, a door and the Minotaur. Ariadne’s string starts at the door, and a tap on a dot lays the next step to it. Every step has to be longer than the one before, the string may never touch itself, and reaching the Minotaur ends it. The question is how many steps the way in can take. Each string that reaches him is kept on a wall by the board, one for each number of steps, and the board never says how many the best one has: it shows a dashed frame while a longer way exists.

The rules

Walk Ariadne's string from the door to the Minotaur in as many steps as you can.

A small room of dots with a door in one corner and the Minotaur in the next. A string is laid from the door one step at a time, each a little longer, until it reaches the Minotaur in four steps.
The string starts at the hole. Tap a dot to step to it. Reaching the Minotaur ends the string.
The string has taken a step of root two, and a circle that size sits round its end. Another step of root two is struck out in red; a step two across and one down, root five, lands outside the circle and is taken.√22121√5
Every step must be longer than the one before. 2 across and 1 down is 2² + 1² = 5: a step of √5.
A step is offered that would cut back across the string already laid. It is struck out in red, and a step that stays clear of the string is taken instead.
The string may never touch itself.

What it gives you to practise

Lengths that cannot be read off a ruler. A step two across and one down is the long side of a right triangle, 2² + 1² = 5, so it is √5 long, and whether it beats a step of 2 or of √8 is a question about those sums. Help draws the last step’s triangle with its sides numbered and marks every dot the string can still reach.

In a classroom

Gordon Hamilton, MathPickle, 2015, from his Grade 8 sheets, where the room is 5 × 5 with the door in the top corner and the Minotaur in the corner below. Here that room is one of twenty-five: plain rooms from 3 × 3, odd-shaped ones — a ring, an hourglass, a room with a hole in it — and great halls up to 8 × 8. Every room’s best was proved by a computer search through every string, so the longest way in on each board is known. Tap the dot you are standing on to take a step back. The board prints as the bare room, for a pencil.

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The whole puzzle 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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Near it on the shelf