El grano de arroz
- Duplicar y potencias
- Ages 8 to 14
- About 7 minutes
The story behind it
An old Indian legend says the inventor of chess asked his king for a reward that sounded tiny: one grain of rice on the first square, two on the second, four on the third, doubling to the end of the board. The king laughed. Then his treasurers did the sum.
Read the full story: The king who could not pay →How to play
- Tap each square in turn to lay the rice.
- Every square holds twice the one before.
- Use the board to answer Ashta’s questions.
Levels
For teachers and coaches
Grain of rice — Doubling and powers
Ages 8 to 14 · about 7 minutes · 8by8verse Chess Lab
What it teaches
Repeated doubling, powers of two, and how quickly exponential growth leaves ordinary counting behind.
The story to tell first
An old Indian legend says the inventor of chess asked his king for a reward that sounded tiny: one grain of rice on the first square, two on the second, four on the third, doubling to the end of the board. The king laughed. Then his treasurers did the sum.
Three questions to ask
- The total so far is always one less than the next square. Can you see why?
- Which is more: a thousand grains a day for a year, or the rice on square 20?
- Where else does something double again and again?
Without a screen
Fold a sheet of paper in half, then again, and count the layers each time. How many folds before you cannot fold it?
Siguiente
Finish
Hint
Step back
Start again
Play again
Next level
Back to the lab
Right.
Not quite.
Not yet — have another go.
Question {n} of {total}
{right} out of {total} right.
Three stars. Clean work.
Two stars. Well played.
One star. Level done.
king
queen
rook
bishop
knight
pawn
Tap square {n} to lay its rice.
Square {n}
Grains on this square
Grains on the board so far
Fill the row
Fill the whole board
About a handful of rice.
About a large sack of rice.
More than a lorry can carry.
A whole shipload of rice.
A mountain of rice — more than any kingdom ever stored.
More rice than the whole world grows in hundreds of years.
How many grains are on square 8?
Start at 1 and double seven times: 128.
How many grains are on the whole first row together?
1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 = 255. That is one less than the next square.
How many grains will square 9 hold?
Double 128: 256.
Which square is the first to hold more than a thousand grains?
Square 10 holds 512. Square 11 holds 1,024.
Which square is the first to hold more than a million grains?
Square 21 holds 1,048,576.
How many grains are on square 10?
Square 9 holds 256. Double it: 512.
Squares 1 to 5 hold 31 grains together. How many does square 6 hold?
Each square holds one more than everything before it: 32.
Each square holds the one before it multiplied by what?
Doubling means multiplying by 2.
Square 16 holds 32,768. How many does square 17 hold?
Double 32,768: 65,536.
The last square holds 2 multiplied by itself how many times?
Square 1 is 1, square 2 is one doubling — so square 64 is 63 doublings.
Which of these is the total for the whole board?
The total is always one less than the next doubling: 2 to the power 64, take away 1.
How many squares hold more than a million grains?
Squares 21 to 64 — that is 44 squares.
Doubling ten times multiplies a number by about how much?
Ten doublings make 1,024 — about a thousand.