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Beads and Bags

Age 5 to 11 Challenge Level:

Thank you to those of you who sent in solutions to this problem.  Class 6 from WPS wrote:

$3$ bags, put $1$ bead in each of the $3$bags
$2$ bags, put $2$ beads in one of the bags and $1$ bead in the other bag.  

Nihaarika from Wellington Primary School thought about the idea of putting bags inside bags.  She said:

Put one bead in each of the three bags.
Then, put the three bags into another three bags.
Continue putting the bags into three other bags.
Thus, you will need $9$ bags.
This can also continue on and on.

Ellie and Caroline from FES in the USA thought very creatively about this problem.  Here are their suggestions:

We can not decide which ones of our solutions are best but some of them are very weird.

1. $3$ beads in one bag
2. $1$ bead in each of three bags
3. $2$ beads in one bag and $1$ in another bag
4. $1$ bead in a folded bag in another bag which was unfolded containing $2$ beads
5. $2$ beads in a bag that was folded and $1$ bead in an unfolded bag that contains the folded bag
6. $2$ beads in separate folded bags contained in one unfolded bag with $1$ bead in it
7. $3$ beads in one folded bag contained in one empty unfolded bag

They then went on to list more possibilities which used different types of bags!  I think we were assuming that the bags would all be the same kind of bag, or that the kind of bag wouldn't matter, but I'm really pleased you thought hard about the problem.  Really well done.

I think perhaps there is one combination that Ellie and Caroline have missed off, although  as Nihaarika says, we could just keep putting each bag into another empty bag.   What do you think?