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'The Thousands Game' printed from http://nrich.maths.org/
You had to think very carefully to answer this
question. Amy from St Albans Primary School, Kevin from CIS, Hong
Kong, Kirsty who goes to Steeple Morden and Ruth all reasoned it
through very clearly. Here is Amy's argument:
When Jill did it, she picked out $7, 8, 6$ and $3$. To make the
biggest even number she got $8736$. Vincent picked out $4, 2, 9$
and $1$. The biggest even number is $9412$. Vincent won because he
had the highest even number. I worked this out because $9000$ is
bigger than $8000$.
Next it was the highest odd number. Belinda picked out $4, 0, 6$
and $9$. The highest odd number from these is $6409$. Ali picked
out $5, 2, 1$ and $7$. His highest odd number is $7521$. Ali's
number is higher than Belinda's because $7000$ is higher than
Next is the lowest even number. Ben picked out $7, 0, 3$ and $9$
and the lowest even number is $3790$. Rohan picked $8, 1, 5$ and
$4$ and his number is $1458$. Rohan won because $1000$ is lower
Alice got $7, 8, 4$ and $9$ and Chloe got $1, 0, 3$ and $5$. The
numbers they got which are nearest to $5000$ are $4987$ and $5013$.
I used an abacus to show that the difference is $13$ for both and
so it is a draw.
Thank you for a very clear solution, Amy.