Which corner can you reach?
Start bottom left. Reach a different corner, using exactly twice as many vertical steps as horizontal steps.
The clock starts when you reveal the puzzle.A JOURNEY WITH A HIDDEN CONSTRAINT
Twice up and down.
Once left and right.
Draw a route.
Discover its destination.
VERTICAL ↕0
= 2 ×HORIZONTAL ↔0
Tap a square in the same row or column, or drag along a route. Each square counts as one step.AT YOUR OWN PACE
A brain snack, with room to think.
THE ANSWER OPENS ANOTHER DOOR
Now for the lovely part.
You have an answer. Explore how it works, then take the idea somewhere new.
See why it works ↓Keep your time
THE IDEA BEHIND YOUR ANSWER
The route was yours.
The corner was forced.
Replay your unit steps, then see why no amount of wandering can change the possible corner.
LOOK AT ODD AND EVEN
Every vertical step changes row parity.
Start in the bottom row. Each vertical step toggles whether you are an even or an odd number of rows away. Horizontal steps leave that unchanged.
Twice any whole number is even. Your number of vertical steps is therefore even. You must finish an even number of rows from the bottom.
The two top corners are seven rows away—an odd number. Both are impossible. The starting corner is excluded by the rules. That leaves only the bottom-right corner.
A possible route completes the argument.
Go up seven squares, right seven, then down seven. That is 14 vertical and 7 horizontal steps. It reaches the required corner and obeys the ratio.
Any route to that corner needs at least seven horizontal steps, hence at least fourteen vertical steps. So 21 total steps is also the shortest possible. Longer valid routes count too.
The idea to take away
Instead of tracking every move, track what each move changes. Parity can rule out destinations before you draw a route.