The rice and the chessboard

A demo of what educators can make with Claude. The rice and chessboard story is an example topic, and the content is quick and unchecked.

The idea: exponential growth

One grain on the first square, two on the second, four on the third: each square doubles the one before. That rule is an example of exponential growth.

Most things we count grow by adding: one more, then one more again. Exponential growth multiplies instead. Something grows by the same proportion at every step, so the bigger it gets, the faster it grows.

At first the numbers look tiny, which is exactly why exponential growth is so easy to underestimate. Because each step doubles what is already there, every square holds one more grain than all the squares before it combined.

For comparison, if each square simply added one more grain than the last (1, 2, 3, 4 and so on), the whole board would hold just 2,080 grains, about 52 grams of rice.

Move through the board at your own pace and watch what the rule does.

Your guess stays on this page only.

From square 33 there is too much rice to draw, so the squares are shaded gold, and each count is shown as a power of 2. The current square has a white outline and a red label.

Jump to

Square 1

Grains on this square
1
Grains in total so far
1
Weight of the total
25 mg
Roughly the same as
a single grain

Grains on each square

Why it matters

The rice doubles on every square, but anything that grows by a fixed percentage doubles at a fixed interval too. Savings, debt and the spread of an infection all follow the same pattern.

Over 40 years

Savings at 7% a year double in about 10 years.

Over 16 years

A debt at 20% a year doubles in under 4 years.

Over 30 days

Infections doubling every 3 days grow about a thousandfold in a month.

Each dot marks a doubling. The dots are evenly spaced because the doubling time never changes.

A period can be a year, a day or any other step. A handy shortcut, the rule of 70, estimates the doubling time as 70 divided by the percentage.

Exponential growth looks harmless at first. That is what makes it so easy to underestimate.

Change the assumptions

The grain counts are exact. The weights depend on how heavy a grain of rice is, so try changing it.

Real grains vary, roughly 20 to 30 mg.

World rice harvest per year

About 553 million tonnes of milled rice, the FAO’s forecast for 2026/27 (September 2026).