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PrintSouth African Mathematics Olympiad
South Africa number theory
Problem
Marks are drawn on a thin strip of paper dividing the strip into 4 equal lengths. Marks are also drawn dividing the strip into 3 equal lengths. After the strip has been cut at each mark, how many pieces will there be?
Solution
6 If the length of the strip is 12 units, marks will be made at 3 units, 6 units and 9 units for four equal lengths, and at 4 and 8 units for the three equal lengths. This gives 5 marks in all, meaning there will be 6 pieces when the cuts are made.
Final answer
6
Techniques
Least common multiples (lcm)