St Ives
How many people were going to St Ives?
Problem
You might have heard this riddle before, which dates back to the 18th century:
As I was going to St Ives, I met a man with seven wives, Each wife had seven sacks, Each sack had seven cats, Each cat had seven kittens: Kittens, cats, sacks, and wives, How many were going to St Ives? |
Some people interpret this as meaning that only the narrator is going to St Ives, and everybody else in the riddle is leaving it. Other people argue that everybody in the riddle is going to St Ives, and they all meet on their way there.
If everybody is going in the direction of St Ives, how many people, cats, kittens and sacks would this be, including the narrator and the man?
There's an older version of this problem on the Rhind Mathematical Papyrus, which dates back to around 1650 BC:
| A house inventory | |
| houses | 7 |
| cats | 49 |
| mice | 343 |
| spelt | 2,301 |
| hekat | 16,807 |
| Total | 19,607 |
We don't know what story was told around this problem, but can you see how it might have been similar to the St Ives riddle?
There was a mistake on the papyrus, which we've left in the table above. Can you find it?
Can you make up your own riddle like these ones for a friend to solve? (Remember to work out the answer so you can tell them if they're right or not!)
Teachers' Resources
Why do this problem?
This problem provides an opportunity for learners to practise multiplying large numbers by 7 within the context of solving a puzzle.
Possible approach
Allow some time for learners to tackle the St Ives problem as stated. The second part of the problem should be straightforward once they've finished the first part, as children should (hopefully!) be able to look back through their workings to find out which power of 7 is incorrect in the table.
Key questions
How many sacks/cats/kittens is that? What could you do to find out?
Can we draw a diagram of what's happening to make it clearer?
Possible support
Some children will need support with the multiplication, and might benefit from having access to a multiplication grid if they aren't confident with their 7 times table.
Possible extension
Children might like to make up their own riddles, as suggested in the final question on the problem page. Encourage them to stick to the formula by choosing a multiplication table and going up in powers of that table.
Some children might like to investigate the full problem from the Rhind mathematical papyrus, which illustrates that $$(2^0 + 2^1 + 2^2)(7^0 + 7^1 + 7^2 + 7^3 + 7^4) = 7^1 + 7^2 + 7^3 + 7^4 + 7^5$$