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3. Lighthouse A flashes once every 12 seconds. Lighthouse B flashes once every 14 seconds. How often do they flash together? Suppose they just flashed together. The table shows their flashes after that instant. 988470564228140B 847260483624120A They flash simultaneously every 84 seconds [The solution to the problem is the L.C.M. of 12 and 14]

4. © T Madas Lighthouse A flashes once every 12 seconds. Lighthouse B flashes once every 14 seconds. Lighthouse C flashes once every 15 seconds. How often do they flash together? They flash simultaneously every 7 minutes

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6. Michael and Ralph Shoemaker are Formula 1 drivers. They start together on the starting line. Michael laps continuously at 1 minute 20 seconds. Ralph laps continuously at 1 minute 30 seconds. How long does it take Michael to be a whole lap ahead of Ralph? How many laps has each of them covered at that moment? Michael laps Ralph minutes from the start 12 Formula 1 Racing

7. © T Madas Michael and Ralph Shoemaker are Formula 1 drivers. They start together on the starting line. Michael laps continuously at 1 minute 20 seconds. Ralph laps continuously at 1 minute 30 seconds. How long does it take Michael to be a whole lap ahead of Ralph? How many laps has each of them covered at that moment? Michael: 720 ÷ 80 = 9 laps Ralph: 720 ÷ 90 = 8 laps Formula 1 Racing

8. © T Madas A n u n u s u a l p r o b l e m

9. © T Madas An equilateral triangle coloured as shown sits on top of a square whose side length is the same as that of the triangle. The triangle topples around the square as shown How many topples does it take until the triangle and square have the same starting position? A n u n u s u a l p r o b l e m

10. © T Madas A n u n u s u a l p r o b l e m Let’s go back to the starting position

11. © T Madas A n u n u s u a l p r o b l e m solution

12. © T Madas 1 A n u n u s u a l p r o b l e m solution

13. © T Madas 2 A n u n u s u a l p r o b l e m solution

14. © T Madas 3 A n u n u s u a l p r o b l e m solution

15. © T Madas 4 A n u n u s u a l p r o b l e m solution

16. © T Madas 5 A n u n u s u a l p r o b l e m solution

17. © T Madas 6 A n u n u s u a l p r o b l e m solution

18. © T Madas 7 A n u n u s u a l p r o b l e m solution

19. © T Madas 8 A n u n u s u a l p r o b l e m solution

20. © T Madas 9 A n u n u s u a l p r o b l e m solution

21. © T Madas 10 A n u n u s u a l p r o b l e m solution

22. © T Madas 11 A n u n u s u a l p r o b l e m solution

23. © T Madas 12 A n u n u s u a l p r o b l e m solution

24. © T Madas 12 A n u n u s u a l p r o b l e m It takes 12 topples Mathematically we are looking for the L.C.M. of 3 and 4 What would the answer be if we had a dodecagon toppling over an octagon?

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