Can you solve it? Bongard picture puzzles that will bongo with your brain

Hello guzzlers.

In the following picture the six images on the left conform to a pattern, or rule, and the six images on the right conform to a different pattern, or rule.

Facebook Twitter Pinterest Problem by M. M. Bongard. Illustration: www.foundalis.com

On the left: triangles. On the right: quadrilaterals. Easy!



The Soviet computer scientist Mikhail Bongard, who was interested in pattern recognition, devised this style of problem in the mid nineteen sixties. There are always 12 images, six on either side. Often the rule for the right hand set of images is simply the negation of the rule on the left.

Today’s puzzles are five Bongard problems. The first is by the man himself.

Facebook Twitter Pinterest Problem by M. M. Bongard. Illustration: www.foundalis.com

Not so difficult, I hope. But the next one is trickier:

Facebook Twitter Pinterest Problem by Harry Foundalis. Illustration: www.foundalis.com

This last one was devised by Harry Foundalis, whose double PhD in cognitive science and computer science at Indiana university was concerned with the cognitive architecture required to solve Bongard problems. He maintains a fantastic online database of Bongard problems. (But don’t go there for the answers, since you won’t find them!)

This next one is also by Foundalis.

And no, the rule on the left is not that the lines are all parallel, since one of the boxes on the right has parallel lines.



Facebook Twitter Pinterest Problem by Harry Foundalis. Illustration: www.foundalis.com

Bongard problems were popularised in Gödel, Escher, Bach, the 1979 bestseller by Douglas Hofstadter.

I’ll leave you with two extremely fiendish ones by Hofstader, who was also Foundalis’s PhD supervisor.

The rule in both cases is very simple - but spotting it is not!

Facebook Twitter Pinterest Problem by Douglas Hofstadter. Illustration: www.foundalis.com

Facebook Twitter Pinterest Problem by Douglas Hofstadter. Illustration: www.foundalis.com

I’ll be back with the answers at 5pm BST today. And no spoilers please in the comments below.

UPDATE: Just to be clear, I am asking you to find the rule that connects the left six images in each set of 12, and the rule that connects the right six images. Sorry if this was left ambiguous - Alex.

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Thanks to Harry Foundalis.

I post a puzzle here on a Monday every two weeks.

My most recent book is the mathematical colouring book Snowflake Seashell Star. (In the US its title is Patterns of the Universe.)

You can check me out on Twitter, Facebook, Google+ and my personal website.

And if know of any great puzzles that you would like me to set here, get in touch.