On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
Stage: 2 Challenge Level:
Excellent solutions were received from several of you including Heather from Stow Heath Junior School, Konrad from Baulkham Hills High and Richard from Sullivan School. Heather explains how you might go about finding the odd box:
Take one coin from the first box, two coins from the second box and so on.
You will end up with 55 coins taken from the various boxes. Weigh the 55
coins. If the weight reads one gram less than 550 then 1 coin weighs 9
grams and box number 1 contains the light coins. If the weight reads 2
grams less than 550 then two coins weigh 9 grams and box number two
contains the light coins and so on.
Konrad puts it a slightly different way:
The last digit of the weight will tell you which box has the 9g coins in
If the last digit is 9 then the box you took 1 coin out of is the box you
are looking for. If the last digit is 8 then the box you took 2 coins out of is the box you
are looking for. If the last digit is 7 then the box you took 3 coins out of is the box you
are looking for and so on.
Thank you to everyone for your solutions and sorry that we can't mention you all.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.