Cubes

Cubes are wonderful things. With six side surfaces, eight vertices and 12 edges, they are highly symmetrical. There are 11 ways to flatten a cube into a plane by cutting the edges. Here are 6 of the 11 ways:

Can you tell which cube is different? You can ignore the orientation of the letters – they are merely for identification. The symbols have been added for those readers who are colourblind.

If you are puzzled, we have a solution for you.

Did you know?
The subiculum plays a role in spatial navigation, mnemonic (symbol) processing. You probably already understood that this puzzle challenges the 3D representation facilities of your brain.

Playing with numbers – quickies

The next two problems are variants of easy problems from the Dutch 2008 Mathematics Olympiad.
1) 2016^*
What is the smallest integer number that, when multiplying its digits, gives 2016?

2) Odd numbers ^*
Multiply all numbers between 1913 and 2012 (including 1913 and 2012). What is the last digit of the product?

You can check your solutions at 16 and 26 respectively.

Books

1) books^*
The professors assistant entered the office room of the professor and noticed that the professor had not only labeled the plants as shown in a previous post, but also his books. Only a new book on his desk was not yet labeled. Can you help him out?

You can look up hint here.

As you may have noticed I like this type of puzzle. Though I am no brain expert, i think you need to active different parts of your brain, and though I’m no expert in the field here’s a list of those parts of the brain which i think will be utilized while solving these puzzles:

• According to research by J. R. Binder and others, the Angular gyrus was used heavily when processing abstract keywords. Finding the correct abstract concepts play an important role in these puzzles.
• Prefrontal Cortex: used for: planning, reasoning, and judgment. Once you have an idea which properties of the objects play a role in the codes, you will need deductive reasoning to check that. Deductive reasoning activates the left frontal lobes, as researched in a meta study in 2011 by Jérôme Prado, Angad Chadha, and James R. Booth.
• The Occipital Lobes are used by visual activities, and as these puzzles are highly visual the solver needs to use this part of his/her brains.
• The inferior frontal gyrus and middle temporal gyrus are utilized according to research by Jing Wang, Julie A. Conder, David N. Blitzer, Svetlana V. Shinkareva.
• Corpus Callosum: This allows information to move between the left and right hemispheres of the brain and is thus a very important integrative structure.

Next weekend we hope to be away a few days, so the puzzle may be later than usual.

Fractions

1) Which Fraction is missing?^*

You can check your solution.