What it does
Doubling looks slow at first and then runs away. Two classic puzzles show it:
- Fold paper. A 0.1 mm sheet folded n times has 2ⁿ layers. Slide n and watch a marker climb a ladder of heights, from a fingernail to Everest, the Moon and beyond. Each step is ten times the one below (a log scale).
- Chessboard grains. 1 grain on square one, 2 on the next, 4 on the next. Tap a square to see its grains and the running total, counted exactly.
A Level switch adds the Class 11 view: the geometric series 1 + 2 + 4 + … and the folds worked out with log₂.
It fits Class 8 Mathematics, power play (powers and very large numbers). Related: exponent laws for the rules of powers, arithmetic progression staircase for sequences, and population growth models for doubling in living things.
How to use it
- Pick Fold paper or Chessboard grains.
- Fold paper: drag n (up to 100) and change the thickness if you like. Landmarks you pass turn green.
- Chessboard: tap a square or slide k.
- Read the formula lines; they show the live numbers.
A worked example
At 10 folds: 2¹⁰ = 1,024 layers, 0.1 mm × 1,024 = 10.24 cm. The Moon (384,400 km) needs just 42 folds: 2⁴² × 0.1 mm = 439,805 km, while 41 folds give about 220,000 km. With logs: n ≥ log₂(3.84 × 10¹²) ≈ 41.8, so n = 42.
On the board, square 10 holds 2⁹ = 512 grains and squares 1 to 10 hold 2¹⁰ − 1 = 1,023. The whole board holds 2⁶⁴ − 1 = 18,446,744,073,709,551,615 grains.
Check yourself
Four fresh questions each time: thickness after folds, grains on a square, grains on several squares, and the fewest folds to pass a height. Press Check; open the worked answer if needed. Nothing is saved.
FAQ
Can you really fold paper 42 times? No. Real paper stops at about 7 or 8 folds. The puzzle is about the maths.
Why are the counts exact? The page uses whole-number arithmetic with no rounding.
Is this from the NCERT book? It covers the same topic with fibub’s own pictures and examples. fibub is not part of NCERT.
Where the numbers come from
- Powers of 2, exponential growth and the sum of a geometric series are standard mathematics. The paper-folding and chessboard puzzles are old folk puzzles. Wording, pictures and examples are fibub's own.
- Ladder heights are well-known round figures: Qutub Minar about 73 m, Mount Everest 8,849 m, the space station about 400 km up, the Moon's average distance 384,400 km, 1 astronomical unit about 150 million km, Proxima Centauri about 4.2 light years. A grain of rice at 0.02 g is a rough round figure you can change.
- Checked against Python's exact integers (2**k and 2**k − 1 for every square 1 to 64) and math.log2 for the folds needed to pass each landmark.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-10.