| home      | people     | research     | publications    | seminars    | events     | contact

### 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.

### Links

 Hamilton Institute - National University of Ireland Maynooth - Co. Kildare - Ireland Tel. + 353 (0) 17086100 - Fax. +353 (0) 17086269 - email hamilton@nuim.ie