Parabola, a wonderful Australian maths magazine for secondary school pupils, celebrates its 60th birthday this month. Today’s puzzles are taken from a recently published compilation of its best problems.
1. The question with no question
(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 squares
Pegs are arranged in a rectangular grid on a board. Rubber bands can be placed around the pegs to form geometrical shapes. The figure above shows how to construct squares of area 1 and 5 using pegs and rubber bands.
Show how to construct squares of areas 8 and 10.
[Knowledge of the Pythagorean theorem may be useful.]
3. Groucho marks
Alexander, David, Esther, Jacinda and Simon all received different marks in the maths test which was held unexpectedly last week. In the following dialogue, either students are truthful or not, and those students who made correct statements invariably had obtained higher marks than those who made incorrect statements.
Simon: Alexander and Esther gained the top two places.
Jacinda: No, what Simon just said is wrong.
David: I was ranked in between Simon and Jacinda.
Alexander: Jacinda came second.
Jacinda: I scored fewer marks than Esther.
Esther: Exactly three of the previous five statements are correct.
Find the order in which the students finished.
I’ll be back at 5pm UK with the solutions. NO SPOILERS PLEASE
Instead, please discuss your favourite clever Australians.
The first issue of Parabola came out in July 1964, published by the University of New South Wales, Sydney. It continues to exist online as a free resource. Aimed at sixth form students (ages 16-18), teachers and enthusiasts, it has the format of a scholarly journal, with fascinating papers on a wide variety of mathematical fields.
Happy 60th birthday Parabola! If you are in maths education, you will find it a unique and remarkable magazine, a treasure trove of interesting material and brilliant problems, more than 300 of which are in Parabolic Problems.
Thanks to Thomas Britz, Parabola’s editor.
I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
My new book, Think Twice: Solve the simple puzzles (almost) everyone gets wrong (Square Peg, £12.99), is out on September 5. To support the Guardian and Observer, order your copy at guardianbookshop.com. Delivery charges may apply.