Schools Mathematics Grand Challenge
Second Week's Puzzles
Problem 3:
The thrid problem was:
A bag contains 28 red, 31 green, 36 black,
29 orange and 27 yellow wine gums. Michael has
been blindfolded so that he cannot see into
the bag. What is the l east number of wine
gums that Michael must choose from the bag to
guarantee tha t he has chosen at least two of
the same colour?
Solution:
The number of wine gums of each colour is
not relevant here. What matters is t hat there
are five colours in the bag. If Michael picks
out five wine gums, he could have one of each
colour. If Michael picks out six wine gums then
at least two of them must be the same colour.
Hence the answer is 6.
Problem 2:
The second problem was:
The total cost of a box of chocolates
is 11 euro - this includes the cost of th e
chocolates and the cost of the box. If the box
costs 7 euro less than the cho colates, how much
do the chocolates cost?
Solution:
If X is the cost of the chocolates then the box
costs 7 euros less which is X - 7.
The total cost of box + chocolates is 11 meaning that
X + X - 7 = 11
giving 2X = 18, and X = 9. So the chocolates cost 9 euro.
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