Parabola, a great Australian maths magazine for high school students, celebrates its 60th birthday this month. Today’s puzzles are taken from a recently published compilation of his 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. Pin blocks**

Pegs are arranged in a rectangular grid on a board. Rubber bands can be placed around the pins to form geometric shapes. The figure above shows how to construct squares of areas 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 points**

Alexander, David, Esther, Jacinda and Simon all got different marks in the maths test which was held unexpectedly last week. In the following dialogue, students are either true or false, and those students who made correct statements always scored higher 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.

**Alexander**: Jacinda came second.

**Jacinda**: I scored less 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

Please book your favorite smart Australians.

The first issue of Parabola appeared in July 1964, published by the University of New South Wales, Sydney. It continue to exist online as a free resource. Aimed at sixth form students (ages 16-18), teachers and enthusiasts, it has the format of a trade journal, with fascinating papers on a wide variety of mathematical fields.

Happy 60th Birthday Parabola! If you are in mathematics education, you will find this a unique and remarkable magazine, a treasure trove of interesting material and brilliant problems, of which over 300 in *Parabolic problems. *

*Thanks to Thomas Britz, Parabola’s editor. *

*I’ve been doing a puzzle here on alternate Mondays since 2015. I’m always on the lookout for great puzzles. If you want 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 5 September. To support the Guardian and Observer, order your copy from guardianbookshop.com. Delivery charges may apply.*