Paper Folds
一张纸厚0.1毫米,每折一次翻倍 · 猜猜折几次能到长颈鹿、珠峰或月球的高度
一张纸只有 0.1 毫米厚，但每次折叠都会使厚度翻倍。这堆叠的高度增长有多快？
需要折叠多少次才能让这张纸的厚度达到 长颈鹿 的高度？
为什么这么少: 翻倍增长惊人快速 · 0.1 毫米的纸张折叠 42 次即可到达月球。
About Paper Folds
Paper Folds is a small lesson in how fast doubling runs away from you. A sheet of paper is about 0.1 mm thick, and every time you fold it in half the thickness doubles. The game names a real object · a giraffe, the Eiffel Tower, Mount Everest, the Moon · and asks how many folds it would take for the stack to reach that height. Four choices; pick the closest.
The answer is exact maths, not a guess. The number of folds is the smallest whole number of doublings that reaches the target height: ceil(log2(height ÷ 0.1 mm)). Because the growth is exponential, the answers are absurdly small · a giraffe takes about 16 folds, Everest about 27, and the Moon a mere 42. The reveal shows the object's real height and the fold count every round.
Build a streak. Each correct answer grows your streak and your best is kept, so a run trains your intuition for exponential growth · the same maths behind compound interest and viral spread.
Part of the PlayMemorize family · runs entirely in your browser and works offline as a Progressive Web App.
FAQ
-
How is the number of folds worked out?
A sheet of paper is 0.1 mm thick and every fold doubles it, so the height after n folds is 0.1 mm times two to the power n. The answer is the smallest whole number of folds whose stack reaches the target height · mathematically, the ceiling of log base 2 of the height divided by 0.1 mm. -
Does folding paper 42 times really reach the Moon?
In theory, yes. 42 doublings of a 0.1 mm sheet is about 440,000 km, which clears the average Earth-Moon distance of roughly 384,400 km. In practice you cannot fold ordinary paper more than about seven or eight times · the game is about the maths of doubling, not a folding challenge. -
Are the object heights real?
Yes · they are the widely-cited real heights or distances for each object, from a giraffe at about 5.5 m to the edge of space, the Space Station and the Moon. The reveal shows the height it used. -
Why do such tall things need so few folds?
Because doubling is exponential. Ten folds already gives about ten centimetres, twenty folds about a hundred metres, thirty folds about a hundred kilometres · each ten folds multiplies the height roughly a thousandfold, so even huge heights fall within a few dozen folds. -
Does it work offline?
Yes. PlayMemorize is a Progressive Web App, so Paper Folds keeps working without a connection once the page has loaded. -
Can MemPi help me study and practice this game?
Yes! Click MemPi in the header or on the game board to summon him. He observes the board, thinks out loud, and can demonstrate moves or guide you through tricky steps.