We had ideas from the Inter School in Zurich,
Moorfield Junior School, Higher Bebington Junior School on the
Wirral, Yarm Primary School, Cummersdale School in Carlisle as well
as from students in Etobicoke, Ontario, Canada. There was quite a
range of answers for this problem, from four ways to $740$ ways to
put the ten coins into the plum puddings!
Here's what Tom did. He was very systematic,
so we know that he has counted all the possibilities and hasn't
counted any twice.
I know that each pudding must have at least two coins.
No pudding can have more than six coins, or there wouldn't be
enough left for the other two.
If one pudding has six coins, then the other two must each have two
coins, and that uses all ten.
If one pudding has five coins, then one of the others must have
three and the other two.
If one pudding has four coins, then either another could have four
and the third just two, or the remaining two could have three
If no pudding has four or more coins, then we wouldn't have used
all the coins. So these four possibilities are the only ones.