Balance

Balance is a weight puzzle shaped like the hanging mobiles you see above a baby’s cot. A beam hangs from the ceiling by a string; from its hooks hang stones, or more beams with stones of their own. Some hooks are empty, and below the mobile sits a tray of numbered stones. Your job is to hang the stones so that every beam in the mobile is perfectly level.

There is one rule, the one every see-saw follows: a beam is level when weight × distance is the same on both sides of its string. A stone of 2 three steps out balances a stone of 3 two steps out on the other side, because both make 6. The beams themselves weigh nothing, but a beam hanging from a hook weighs everything that hangs below it — and that is where the thinking starts, because the beams depend on each other.

Puzzles grow with the difficulty: three empty hooks for easy, four for medium and five or six, on up to four beams, for hard. Some beams carry three hooks, two on one side, so their sides have to be added up. And the tray always holds a stone or two too many — part of the puzzle is finding which stones belong on the mobile at all. Our server makes every puzzle and tries every possible way of hanging the stones before anyone sees it, so each one has exactly one answer.

How to start a game

1. 1Open Balance on Alex Play Zone and press Start Puzzle; the clock starts when the mobile appears.
2. 2Drag a stone from the tray onto an empty hook — or tap the stone, then tap the hook.
3. 3Drop a stone on a hook that already has one and the two swap places. Drag a stone back to the tray to take it off.
4. 4Watch the beams: each one tips towards its heavier side as stones go on, and turns green when it is level with all its stones on. It shows you which side is heavy, never the answer.
5. 5Reset takes every stone back to the tray. Hint hangs the right stone on one hook for you.

The rules of Balance

The rules

• Every empty hook gets one stone from the tray, and each stone can be used once. The tray holds one or two stones that belong nowhere.
• Distances are counted in hook steps from the beam’s string: 1, 2, 3 or 4.
• A beam is level when, on each side, weight × distance adds up to the same number. A beam with two hooks on one side adds both.
• A beam weighs nothing itself; a beam hanging from a hook weighs all the stones below it.
• Grey stones with a lock are part of the puzzle and cannot be moved.
• The puzzle is solved the moment every beam in the mobile is level.

A new puzzle every two hours

• One new puzzle is made every two hours, and it is the same for every player.
• You get one go at each puzzle. Leave and come back whenever you like: your grid is kept and the clock only runs while the puzzle is open.
• When the next puzzle arrives, an unfinished one is closed and shows as abandoned in your Battle Log.

Rewards

• The faster you finish, the more XP and coins you earn.
• Up to 35 for an easy puzzle, 55 for a medium and 80 for a hard one.
• Each hint takes 10% off the reward.

How to play well

Start at the bottom

The lowest beam carries only stones, so it is the simplest to read. If its left stone sits one step out and its right stone three steps out, the left stone must be three times as heavy as the right one. That alone often leaves just one pair in the tray that fits.

Then add it up

Once you know what hangs on a lower beam, its total weight is just the sum of its stones — and that total is what the beam above feels at that hook. A beam of 3 and 1 hanging one step out weighs 4 for the beam above it, no matter how its own stones are spread.

Turn distances into ratios

Read each beam as a ratio. Distances of 2 and 1 mean the near side must be twice as heavy; distances of 3 and 2 mean the weights must be in the ratio 2 to 3. Writing the ratio down for every beam turns a guessing game into a short chain of small sums.

Find the spare stones

Add up every stone in the tray and compare it with what the beams need. A beam whose sides must be in the ratio 1 to 3 can only take stones like 1 and 3, 2 and 6 or 3 and 9 — a stone that fits no ratio anywhere is usually the spare one.

Let the tilt talk

The beams tip as soon as stones go on. If a beam drops to the right, the right side is too heavy — swap in a lighter stone there or a heavier one on the left. The tilt never gives the answer away, but it tells you which way to go.

Remember: Start with the lowest beam: it holds only stones, so its two sides tell you how those stones compare. Its total then tells you what the beam above it needs.

Common mistakes

• Assuming every stone in the tray must be used — one or two never are.
• Balancing the top beam first: it depends on everything below it, so it is the last one you can be sure of.
• Forgetting that a hanging beam counts as ONE weight for the beam above — the total of all its stones.
• Counting distance from the end of the beam instead of from its string.
• Stopping when one beam turns green: the puzzle is solved only when every beam is level.

Questions and answers

Is there always exactly one answer?

Yes. Before a puzzle is used, the server tries every way of hanging the tray’s stones and keeps the puzzle only if exactly one of them levels every beam.

Do I need to be good at maths?

Only at small multiplications. Every sum on a beam is weight × distance with numbers up to 9 and distances up to 4 — the real puzzle is working out which stone goes where.

What does a hint do?

It hangs the right stone on the first hook, from left to right, whose stone is wrong or missing. Each hint takes 10% off the reward, and there is a short wait before the next one.

Can I play on my phone?

Yes. Drag the stones with your finger, or tap a stone and then the hook you want it on.