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How to balance Seesaw fast: budget the sides before you place

Eigengames team · 6 October 2026 · 5 min read

▶ Play Seesaw🎯 Try a beam where everything goes on one side

The left side reads 1, the right side reads 45, and you’re holding a 2, two 3s and a 5. The clock started when you placed your first weight. You drop the 5 on the far left, the beam swings, and now you’re doing sums under pressure.

Seesaw gets much easier once you stop reading two totals and start reading one number.

One number: the gap

Every weight pushes its side down by its value times its distance from the pivot. That’s the law of the lever, and it’s exactly what the game adds up: a 4 in slot 3 counts 12 and so does a 6 in slot 2. The beam is level when the two sums match.

So forget the two totals and track the gap: heavy side minus light side. A weight on the light side shrinks the gap by weight × distance. A weight on the heavy side grows it by the same amount. You’re done when the gap is zero and the tray is empty.

The gap also tells you what’s possible. The weights still in your hand can change it by at most their total times 5, because no slot is further out than 5. If the gap is bigger than that, the beam can’t be saved and something you already placed has to move. We call this the reach check, and it’s the most useful sum in the game.

Heaviest first, but only with the reach check

The game page says to place the heaviest weight first. We tested that by letting a program solve 1,000 Normal puzzles by trial and error and counting how many placements it tried before it found a solution. The answer depends on whether you also do the reach check.

Without the reach check, heaviest first is actually worse: a big weight in a bad slot poisons everything after it, and you only find out at the end. With the check, it’s the best of the four. After you place the big weight, you check at once whether the rest can still close the gap, and a bad slot gets rejected straight away. On Hard, with six weights to place, the difference is bigger still: 179 tries against 525.

What doesn’t work is levelling as you go. A program that put each weight, heaviest first, wherever it brought the gap closest to zero solved only 13% of Normal puzzles. A level beam halfway through leaves the small weights with nothing to do.

Budget the sides before you place

Before any weight goes down, decide which side each one is going to. On Normal you place four weights, which allows up to 16 ways of splitting them between the sides. Across our 1,000 puzzles, on average only about 4 of those splits lead to any solution at all. Settle the split first and most of the puzzle is gone before you’ve touched a slot.

The reach check does the splitting for you. Take the puzzle from the opening, Normal seed 565. The fixed weights are a 1 in slot 1 on the left and a 9 in slot 5 on the right, so the right leads 45 to 1 and the gap is 44. The tray holds 2, 3, 3 and 5. If all four go left as far out as they fit, with the 5 in slot 5, the 3s in 4 and 3 and the 2 in slot 2, they add 25 + 12 + 9 + 4 = 50. The left then reads 51 against 45. That’s only 6 more than the gap, so there’s almost no room: nearly everything goes left, and it goes far out.

Now you only need to get rid of 6. There are two kinds of adjustment, and both are quick sums:

• Moving a weight w on the same side from distance a to distance b changes its side by w × (a − b). Swapping two weights between slots changes it by (difference in weight) × (difference in distance).
• Moving a weight w from distance a on one side to distance b on the other changes the gap by w × (a + b).

The second rule finds an answer at once: the 2 moved from left slot 2 to right slot 1 shifts the gap by 2 × (2 + 1) = 6, and both sides read 47. The first rule finds the other answer: rearrange the left as 3, 2, 5, 3 in slots 5, 4, 3, 2 and it adds exactly 44.

Finish with the small weights

The last weight you place has to close the gap exactly, so it has to fit: the gap must be that weight times a free distance on the light side. A 1 can close any gap from 1 to 5, a 2 any even gap up to 10, and a 9 only 9, 18, 27, 36 or 45. That’s why the small weights go last. They’re the fine tuning, and they let a nearly right beam become exactly right.

There’s also a parity shortcut, which the game page states in short form. An odd weight in an odd slot adds an odd amount and every other placement adds an even one. So an odd gap needs an odd number of odd-weight-in-odd-slot placements, at least one. If the gap is odd and your only odd weight is already in an even slot, you know without adding anything that it has to move.

Two more facts from the generator. A Normal puzzle has between 1 and 10 solutions, and any balanced beam wins, so don’t hunt for “the” answer. And the generator throws away puzzles that can be solved by mirroring equal weights, so if you hold two 7s, putting them at the same distance on opposite sides is never the whole answer.

Practice

The practice beam is a Normal puzzle where the right side starts at 73 with nothing on the left. Do the reach check first: four weights, all on one side, and you have to land exactly. Then move weights in and out with the two quick sums until the gap is zero.

Find the gap, check your reach, and keep the 1 for last.

▶ Play Seesaw🎯 Try a beam where everything goes on one side