Number Line Hop

A hand of four operations, five hops, and a flag you have to land on exactly

• 2 player, one device
• puzzle
• numbers
• 2 player

Prefer it full screen? Open Number Line Hop on its own.

About Number Line Hop

A number line runs across the screen with a flag planted on the target. Your hopper starts on zero. Four pads sit in a rail below, each carrying one operation, and choosing one sends the hopper along an arc to the new number. Land exactly on the flag and the round is yours. Land near it and you have spent a hop for nothing.

Five hops is the budget, and the hand you are dealt can always do it in three or four, so the game is about the order rather than the accumulation. A multiply that would have been perfect two hops ago is worth nothing once you have added your way past it.

Arming a pad draws a ghost hopper at the destination with a dashed arc to it, which costs no input and can be changed as often as you like. A hop that would land on a fraction, move you nowhere or leave the line is refused outright with the reason written in the hint line, so the four pads in front of you are never a trap.

Play against the computer at three strengths, or pass the device between two people. Both hoppers share the same hand and the same line on separate lanes, taking alternate turns, and the first to win three rounds takes the match. If neither player lands in five hops, a fresh hand is dealt and the round is replayed with nothing scored.

What is different about this version

The hand is dealt from a solution and then proved again. The game plays three or four random operations forward from zero, takes wherever it ends up as the target, fills the hand out to four distinct pads, shuffles them, and then runs a breadth-first search from zero to confirm the target is reachable — and rejects the round unless the shortest path is exactly three or four hops. That is why five hops feels tight rather than generous: you are given one or two spare moves, never five. The hand is also composed rather than sampled, with at least one add or subtract pad so no player can ever be stuck, at least one multiply or divide so the round is never plain counting, and at most two of the heavy operations. The view is solved the same way, taking the span that contains both hoppers, the flag and any armed destination with a two-tick margin, floored at twenty units, so the answer is always visible before you commit to it.

How to play Number Line Hop

1. Tap a pad to arm it and a ghost hopper appears on the destination tick with a dashed arc.
2. Tap the same pad again, or press Confirm, to take the hop.
3. Land exactly on the flag to win the round. Landing near it does nothing.
4. A pad that would produce a fraction, move you nowhere or leave the line is refused before you spend the hop.
5. Each player gets five hops per round and takes alternate turns on their own lane.
6. First to three rounds wins the match. Nobody landing means a fresh hand and the same round again.

Controls

Desktop	Click a pad or press 1 to 4 to arm it, then click it again or press Enter to commit. Escape or P pauses, and the pause sheet holds the mode and difficulty chips.
Phone or tablet	Tap one of the four pads in the bottom rail to arm it, then tap Confirm. The rail sits clear of the number line so the arc is never under your thumb.
Players	One or two people on the same device. Nothing here plays over the internet.

Strategy

Work backwards from the flag rather than forwards from zero. A target of thirty-nine with a times three pad in the hand is almost certainly thirteen multiplied, so the real question becomes how to reach thirteen, and that is a much smaller problem than searching the whole line. Multiplication and division are the pads that move you a long way and they are also the ones that stop being legal as your position drifts, so spend them early and use the additions to close the gap. The ghost preview is free and unlimited, so arm each pad in turn and read the destination before committing; against the Hard computer, which takes the best hop ninety-two per cent of the time and avoids hops that would kill its own path, the round is usually decided by whoever wastes a hop first. In two-player, remember that both hoppers share one hand, so the route you found is also the route your opponent can see.

Mistakes that cost you the game

• Adding your way toward the flag and saving the multiplier. Multiplying from a large number overshoots, and the pad becomes dead weight.
• Committing without arming first. The ghost hopper and the dashed arc cost nothing and show the exact landing tick.
• Reading a refused pad as a bug. It means the hop would land on a fraction, move you nowhere or leave the line, and the hint line says which.
• Treating a near miss as progress. Only an exact landing wins the round, and the hop is spent either way.
• Forgetting that the target can be negative. The line shows negative numbers and the subtract pads reach them.

Tips

• Factor the target first; a multiply pad usually tells you which number you are really aiming for.
• Spend the multiply and divide pads early while your position is still small.
• Arm all four pads in turn and read the ghosts before you commit to one.
• Every hand can be done in three or four hops, so a plan needing all five is probably the wrong plan.
• Difficulty only applies against the computer; the chips are hidden in two-player mode.

Questions about Number Line Hop

Can a round be unwinnable?

No. Each hand is dealt from a route that reaches the flag and then re-verified by search, and it is rejected unless the shortest path is three or four hops out of the five you have.

What happens if neither of us lands?

The round is replayed with a fresh hand and nothing is scored. Who moves first alternates each round regardless.

How good is the computer?

Easy takes the best available hop forty-five per cent of the time, Normal seventy and Hard ninety-two. When it does not take the best hop it deliberately lands near the flag rather than on it, and Hard also avoids hops that would leave it unable to finish.

Can two people play on one device?

Yes. Switch to 2 Players in the pause sheet and pass the device across on each turn. Both hoppers share the same four pads on separate lanes.

Does it cost anything?

No. Number Line Hop is free to play, runs in your browser, and needs no download, install or account.

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