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# Sissa's Reward

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### Consecutive Numbers

### American Billions

### Triangles to Tetrahedra

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

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Age 11 to 14

Challenge Level

According to an old Indian myth, Sissa ben Dahir was a courtier for
a king. Sissa worked very hard and invented a game which was played
on a board, similar to chess. The king decided to reward Sissa for
his dedication and asked what he would like. Sissa thought
carefully and then said, "I would like one grain of rice to be put
on the first square of my board, two on the second square, four on
the third square, eight on the fourth and so on." The king thought
this was a silly request, but little did he know ...

Below is a chess board with the first few squares filled with grains of rice as Sissa asked for:

Below is a chess board with the first few squares filled with grains of rice as Sissa asked for:

How many grains of rice would there be on the 8th square?

How many grains would you need altogether in order to fill up to the 15th square?

Estimate how many grains you would need in total to
fill the entire board in this way. Explain your thinking.

Perhaps Sissa was cleverer than the king thought!

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?