Robot routes: find the first wrong step

Before you start

Practise following one arrow at a time before trying the timed game. Right and down refer to the board, not to the direction the robot faces.

Work through this example

Start at S in the top-left corner and reach G in the bottom-right. The centre is a rock. Move one cell up, right, down or left; never diagonally or through a rock. Use at most four steps.

Reason step by step

1. The goal is two columns right and two rows down: every route needs at least 2 + 2 = 4 moves. A rock can force a detour on other boards.
2. Try → → ↓ ↓. The positions after each move are (row, column): (1,2), (1,3), (2,3), (3,3). None is the centre cell (2,2).
3. The route reaches the goal in four legal moves. Because four is also the lower bound, this route is shortest on this example board.

A mistake worth understanding

→ ↓ → ↓ has the right overall displacement, but its second move hits the centre rock. The later arrows cannot repair a collision that has already happened.

Try it yourself

Find a different four-step route. Then explain why a three-step route is impossible.

Use the idea in the game

The playable levels have larger boards and different rocks. Read the new step limit, trace the route and remove only the first invalid arrow before rebuilding the remainder.

About & help

These examples were written for Piko Game. Generated game questions may differ. A score describes a game attempt, not mastery of a school curriculum.

Content and corrections

Found an error? Send the page address and the step that needs checking to j565718319@gmail.com。