Parabola, a great Australian mathematics magazine for secondary school students, celebrates its 60th anniversary this month. Today’s puzzle is Recently published compilations Some of the best issues.
1. Questions without doubt
(a) All of the following:
(b) None of the following:
(c) Some of the following:
(d) All of the above.
(e) None of the above.
[Just to reassure you, nothing has been omitted here.]
2. Peg Square
The pegs are arranged in a rectangular grid on the board. Rubber bands can be placed around the pegs to form geometric shapes. The diagram above shows how to create squares with areas 1 and 5 using pegs and rubber bands.
Show how to construct squares of area 8 and 10.
[Knowledge of the Pythagorean theorem may be useful.]
3. Groucho Mark
Alexander, David, Esther, Jacinda and Simon all received different marks in a surprise math test last week. In the following conversations, students were either honest or not, and those who made correct statements always received higher marks than those who made incorrect statements.
Simon: Alexander and Esther took the top two places.
Jacinda: No, what Simon just said is wrong.
David: I was ranked between Simon and Jacinda.
AlexanderJacinda came in second place.
Jacinda: I got a lower score than Esther.
Esther: Three of the previous five statements are true.
Find out the order in which students finished.
I’ll be back at 5pm with the solution, no spoilers please.
Instead, discuss your favourite clever Australian.
The first issue of Parabola was published by the University of New South Wales in Sydney in July 1964. Maintain an online presence A free resource. Aimed at sixth graders (ages 16-18), teachers and enthusiasts, it is formatted as an academic journal and contains fascinating articles on a variety of mathematical subjects.
Happy 60th anniversary Parabola! Anyone involved in mathematics education will find this magazine unique and remarkable, with over 300 questions and a treasure trove of fascinating material and great problems. Parabola Problem.
Thanks to Parabola’s editor, Thomas Britz.
I’ve been putting out puzzles here every other Monday since 2015. I’m always looking for great puzzles, so if you have any suggestions please email me.
My new book, Think carefully: Solve a simple puzzle that (almost) everyone gets wrong (Square Peg, £12.99) is out on September 5. To support the Guardian and Observer, order your copy here. The Guardian BookshopShipping charges may apply.
