crystal clear mathematics logo


Sign up to my Newsletter


Logic and Lateral Thinking

Picture of mouse in a cardboard maze. It has eaten its way through the walls directly to the cheese.Picture of a Maze with a line drawn directly from one side to the other with the word Parkour written underneathSometimes we assume too much when we think.  We place restrictions on our thinking that the ‘rules’ never made explicit.

The mouse in the illustration was under no obligation to follow the maze.  I also have a T-Shirt with the picture at right.  I guess free runners have the skills to leap over tall buildings and …


This page will be used for serious logic questions as well as the more light-hearted and lateral question as well.


Transferring Liquid Between Beakers

Two beakers with different coloured liquids in themYou have a beaker containing exactly 200 mL of pure water.  You have a second beaker containing exactly 200 mL of pure alcohol.

They can mix, but they are chemically different.

You take one teaspoonful of water and drop it in the beaker containing alcohol.  You now take one teaspoonful of the mixture and return it to the beaker of water.

Now, is there more alcohol in the water, or more water in the alcohol?

Answer: Answer to the liquid transfer puzzle.

The Local Barber

Young adult male getting hair cutIn a small country town everyone has regular haircuts.

All haircuts are carried out within the township.  Some people prefer always to cut their own hair.  The others always get the village barber to cut their hair.  The village barber also lives in the town.

Now, just to make the conditions perfectly clear ... no one, except the barber, ever cuts anyone else's hair. And none of the men who cut their own hair ever let the barber touch it.

Question: Who cuts the barber's hair?

Answer: Answer to the village barber question

We were all deeply impressed with Graeme from the very beginning. [Lucas’] confidence radically changed within only 3 weeks of Graeme’s instruction and assistance. I am sure this was largely attributed to Graeme’s infectious passion and love for his subject, and his high personal level of skill, teaching experience and understanding of mathematics. Lucas always found Graeme could explain concepts so knowledgeably and easily, which really did transform Lucas’ appreciation and enjoyment of the subject. Graeme always gave Lucas assistance and time over and above his hour’s tutoring session. Graeme has developed a wonderful relationship and more of a mentoring role which has been of great assistance and value to Lucas as he faces the pressures of his final year of school.  I have no hesitation in recommending Graeme as an outstanding tutor and friend, and a very wise, knowledgeable and capable teacher of the highest calibre.
Sally T (parent, 2005)

See all Testimonials

Sign up to my Newsletter

Copyright © Crystal Clear Mathematics | All Rights Reserved

Website Design: | Photography: