Balances

A new Balances puzzle every day

Everyone gets the same mobile each day, and a new one arrives at midnight your time. Monday and Tuesday are easy, Wednesday, Thursday and Sunday are medium, and Friday and Saturday are the hardest of the week.

Solve it on consecutive days to build a streak, then share your time. A shared result shows your time and how many hints you used, never the solution. It has exactly one solution, and you can reach it by logic alone, with no guessing.

How to play Balances

1. A mobile hangs from the ceiling: bars on strings, with hooks along each bar, the marks under it one step apart.
2. Hang every weight from the tray on an empty hook, one weight to a hook.
3. A bar balances when both sides pull the same. A side's pull is each weight on it times how many steps its hook is from the bar's string, added up.
4. A hook holding a smaller bar carries everything hanging from that bar, as if it were one weight.
5. Make every bar balance at once, and you've won.

Tap a weight in the tray, then a hook, or drag it there. Tap a weight on the mobile to take it back, or drag it to another hook to swap. Bars tip toward their heavier side as you go and hang level when they balance. A bar turns green once every weight on it and below it is in place and it balances, and red if they're all in place and it doesn't. Undo has no limit, and every puzzle has exactly one solution.

Solving tips

• Start at the bottom. A small bar with a weight at each end has only a few pairs of weights that balance it: with arms of 1 and 2, the weight on the short arm is twice the other.
• Add it up. The whole mobile weighs every weight in the tray together, and a bar hanging from a hook weighs everything below it. Totals worked out at the top tell you what the bars below must weigh.
• Look for multiples. A bar hanging 3 steps out pulls a multiple of 3, whatever it weighs, so the other side has to pull a multiple of 3 too.
• Place the awkward weights first. A big weight, or one no other weight pairs with, often fits on only one hook.
• Stuck? A hint points to a hook you can work out next, and says why.