Stack It
Drop books, mugs and rubber ducks from a crane. How tall can your tower get? Back to the game
How to play
An object swings from the crane above your desk: a dictionary, a paperback, a mug, an apple, a rubber duck. Tap, click or press Space to drop it. Each one falls, lands and settles with real physics, so a book dropped off-centre makes the whole tower lean and a round apple rolls if it lands on a slope. Keep stacking. The camera climbs with your tower and height markers tell you what you've beaten: a cat, a door, a giraffe. When the tower falls, it falls in slow motion.
Besides the endless tower there are twelve puzzles (fit these objects inside a frame, build up to the line, hang a book past the edge of the table), an earthquake mode, and a daily set of objects that is the same for everyone today.
The physics of a tower
Every object is a rigid body with a real size, mass and friction. The engine finds where shapes touch, then pushes them apart with tiny impulses many times a second, including friction so a book on a tilted stack can grip instead of sliding. This is the same method used by many physics engines in video games, called sequential impulses.
The rule that decides everything is simple: a stack stands as long as the centre of mass of everything above each level is over the supporting surface. Turn on the plumb line to see it. Tall, thin objects tip at small angles: a book standing on its end (3.5 cm thick, 24 cm tall) falls if tilted past about 8°, while a cube holds out to 45°.
The overhang puzzle
How far can a stack of identical books stick out past a table edge? Put one book per level and slide each one as far as it can go: the overhangs are ½, ¼, ⅙, ⅛ of a book length and so on, the harmonic series. Four books already put the top book completely past the edge, and with enough books the overhang can be as large as you like. With several books per level used as counterweights, mathematicians showed in 2009 that you can do even better.
Real towers lean too
The Leaning Tower of Pisa began tilting while it was being built, because the soil under one side is softer. By 1990 it leaned 5.5°. Engineers removed soil from under the high side between 1993 and 2001, and it settled back to about 3.97°, still leaning, but stable for centuries.
- Drop when the object is right above the centre of the stack, not when it looks centred on the crane.
- Put heavy, flat things low and light, round things high.
- A slightly wider base buys you a lot of height later.
Like building? Try a bridge in ../will-it-hold/ or a chain reaction in ../topple-the-dominoes/.
Questions people ask
- Is Stack It free?
- Yes. It runs in any modern browser on phones and computers, with no download or account.
- Why did my tower fall when it looked balanced?
- A tower falls when the centre of mass of the objects above any level moves past the edge of what supports them, even if each piece looks fine on its own.
- What is the daily tower?
- A set of objects chosen by today’s date, the same for everyone, so you can compare heights with friends.
- How far can books overhang a table?
- With one book per level, the overhang follows the harmonic series and can grow without limit. Four books already reach more than one full book length.
- How tilted is the Leaning Tower of Pisa?
- About 3.97° since the stabilisation work finished in 2001; it leaned 5.5° before.
