4 Problems!
Some problems for you
Use your entry and attack strategies to see if you can solve any of the following problems. Don’t feel obliged to spend more than 15 minutes on any one of them.
Married Couples
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Four mathematicians and their partners went shopping. They found that altogether, they were poorer by $5000. Dr. Hilbert’s partner had spent $100, Prof. Fermat’s partner had spent $200, Euler’s better half had spent $300 and Prof. Galois wife spent $400. As for the mathematicians, Amy spent five times as much as her partner, Ajay four times as much as his, Danny three times as much as his and Idris twice as much as his. What is the last name of each of the mathematicians? |
Tips
Chessboard
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How many squares are there on a chessboard? |
Tips
Bees
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Queen bees share a fascinating relationship with the other bees in the hive.
Male bees hatch from eggs that have not been fertilized, meaning that their mother is a Queen bee and they do not have a father. Female bees, on the other hand, have both a mother and a father. If you trace a male bee’s family tree back for 12 generations, how many other bees will be part of that family tree? How many of these bees will be male? Exclude siblings, aunts and uncles, cousins and second cousings, etc. (problem inspired by Mason, Burton and Stacey, 2010) |
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Painting
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Alma can paint a house in 3 hours, Marvin can paint a house in 5 hours. How long does it take them to paint a house if they work together? |
Tips
Shopkeeper
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You walk into a store and the shopkeeper says “Every time you buy something for $10 dollars, I’ll double the amount you have left.” You take the shopkeeper up on his offer 3 times and end up with 0 dollars. How much did you start with? |
Tips
Passing trains
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At 9pm, Albert leaves Melbourne travelling at a constant speed of 100km/h towards Maryborough. At 10pm, Jean-Paul travels from Maryborough and will arrive in Melbourne at midnight. If the distance is 220km, where will they cross? |
Tips
References
Mason, J., Burton, L. and Stacey, K., 2010. Thinking Mathematically Second Edition. England: Pearson Education Limited.
