Weight Split

Nine numbered weights sit in a tray. Move every one of them onto pan A or pan B so that the two pans weigh the same, then submit. There are nine weights and not eight, which means the two pans can never hold the same number of weights — four and four is not an answer here, and never will be, so the only thing worth counting is the total. The board tells you something the puzzle usually hides: exactly how many different balanced splits this set has. Sometimes there are six and almost anything careful works. Sometimes there is one, and finding it is the whole evening.

It runs entirely on your device: 0 network requests, works offline. No ads, no account, nothing to buy, and no betting, money or prizes of any kind.

1. Focus the board — click it, or press Tab until it is focused.
2. Choose a weight with Left and Right. The cursor stays in one column; the weights are laid out heaviest first, because placing the heaviest one first is the method that works.
3. Send it to a pan with Up for pan A (the top row) or Down for pan B (the bottom row). Enter cycles the same weight tray → A → B → tray if you would rather use one key. Pressing an empty slot with the pointer drops the weight straight into that row.
4. Watch the running totals beside each row, and the line under the board. It names the gap and what would close it: while weights are still in the tray, adding the gap to the lighter pan levels it; once every weight is placed, carrying one across changes the gap by twice its value, so only a weight of exactly half the gap can level it in a single move.
5. Take a weight back with Esc, or start the arrangement again with Z. Both are free.
6. Submit with F when the tray is empty and both pans look level. A submission with weights still in the tray is refused rather than charged — an unfinished answer is not a wrong one.
7. Win when both pans weigh the same. Each wrong submission spends one of your attempts, and the round ends when they run out.

How many attempts you get is set by how many balanced splits the set has: a set with a single answer gives you five, a set with eight gives you two. That same number is the multiplier on the score, so the tight sets are the ones worth playing.

How do you split a set of numbers into two groups with the same total?

Add everything up first. If the total is odd, stop — there is no answer, because half of an odd number is not a whole number and every group total is. If it is even, half of it is your target for each side. Then work from the heaviest number down, putting each one on whichever side is currently lighter. That is the greedy method, and on most sets it lands on or very near the answer, because the big numbers are the ones with no room to be fixed later. When it lands near instead of on, look at the gap: moving a number from the heavy side to the light side takes it off one and adds it to the other, so the gap changes by twice that number. A gap of 8 is closed in one move only by a number worth exactly 4. A gap of 7 cannot be closed by one move at all — the gap is odd and every move changes it by an even amount — so you need to swap a pair instead, one number from each side whose difference is half the gap.

Is every set actually splittable?

Yes, by construction, and this is not a hope — it is how the set is made. The two groups are built first: the game picks a half-total, draws one group of distinct weights adding to it, draws a second group of a different size adding to the same half-total, then merges them and shows you the merged set. A balanced split therefore exists before a single weight reaches the board, and there is no generate-and-reject loop anywhere that could hand you an impossible set on an unlucky run. Every dealt set is then checked again by the exhaustive counter, which never looks at the two groups the generator built, so the guarantee is verified rather than assumed. If you ever lose, the board moves the weights to a split that works, so you can see the arrangement rather than be told about it.

What does the split count mean, and why does it change the score?

Before you start, the game walks all 256 ways of dividing the set that keep the heaviest weight on one particular pan — one representative for each split, since a split and its mirror image are the same split — and counts the ones that come out level. That count is printed as Splits, with a word beside it: unique, tight, open, loose. It is a real measurement, not a difficulty label someone typed in. A set with one split has a single arrangement out of 256 that works and needs actual reasoning; a set with eight falls apart almost however you push it. So the count sets your attempts — fewer answers, more attempts — and multiplies the score, up to eight times for a set with exactly one answer.

Two weights show the same number. Is swapping them a second answer?

No, and the counter agrees with you. Weights are drawn independently for the two groups, so a set can easily hold two 15s. If a split puts one 15 on each pan, exchanging them gives an arrangement that is different in the code and identical on the board, and calling that two answers would be dishonest. The count is taken over the values on each side, not over which physical weight went where, so interchangeable weights collapse into one answer. It is the number you would arrive at counting by hand.

Why nine weights, and not eight or ten?

Two reasons, and both are deliberate. An odd count makes equal group sizes impossible, which kills the beginner's instinct to deal them out evenly and forces every decision back onto the totals — the pans in a finished split are usually four against five, sometimes three against six. And nine is the largest set whose splits can all be counted in a single frame: 256 subsets is instant, which is what lets the count be a printed fact instead of an estimate. Eleven weights would be 1024 subsets, still fast, but the board stops fitting a phone screen long before the arithmetic stops being instant.

Is there any money, betting or in-app purchase in this?

None, and there never will be. The weights are numbers on tiles: no currency, nothing to buy, no wager of any kind, and no gambling mechanic anywhere in the game. The score exists so a good split feels better than a lucky one, and it is not for sale.

Can I play it with a keyboard or a screen reader?

Both. Left and Right choose a weight, Up and Down send it to a pan, Enter cycles through the three rows, Esc takes one weight back, Z clears both pans and F submits. Every weight announces its value and which pan it is on; the board announces both running totals, how many weights are still in the tray, the gap and what would close it, and how many attempts remain. Each tile also carries a glyph — ▲ for pan A, · for the tray, ▼ for pan B — so nothing depends on telling one tint from another, and the row a weight sits in says the same thing again.

Does it work offline?

Yes. Once the page has loaded once, the whole game is on your device — the generator, the exhaustive counter, the rules, this page. Nothing is fetched while you play, and no result leaves the device.

Nine weights, each a whole number from 4 to 36, drawn so that both groups hold at least three. The split count is exact rather than sampled, because 256 subsets is small enough to enumerate honestly; it is counted by value, so identical weights are treated as interchangeable. Attempts run from two to five and the score multiplier from one to eight, both derived from that count. Weights are plain numbers with no unit — nothing in the game depends on their being kilograms, and inventing a unit would only suggest a precision the puzzle does not have. There is no hint button and no partial credit: a split is level or it is not.

Sum Links is the other number game built on adding a subset to a target, but there the cells have to touch, so geometry does half the pruning. Deal Sum asks for four cards that reach a stated total and prices the deal by how many routes exist, which is the same scarcity idea applied to one group instead of two. Balance Scale is the pan balance used the other way round — you are finding a single odd weight rather than dividing a set — and it teaches how much one weighing can possibly tell you.

Bookmark this page (Ctrl+D, or ⌘D on Mac) or install the app — it works offline the next time you need it.