Thinking outside the box: One half of thirteen is eight


With our pattern thinking, we easily get caught up in a habitual way of approaching a problem. In school, we have also been trained to think convergently, i.e. to look for the one and only correct answer, instead of taking a step back, observing the world with non-judgmental eyes and reflecting on unexpected solutions to the problem.

I have previously highlighted this phenomenon in the blog post Thinking outside the box: The Barometer question.

With this strategy, we often come up with appropriate solutions to a problem, but these are often neither very odd nor innovative. Since our brain wants to use as little energy as possible, we usually stick to the first answer that fits our question, and then stop thinking.

The opposite way to address a problem, is instead to try to find as many divergent solutions as possible to a problem that at first glance appears to be convergent. To succeed, we would need to consider the problem from completely new perspectives, i.e. what we sometimes call lateral thinking or thinking outside the box.

An illustrative example of this is the question: “What is one half of thirteen”? Our immediate intuitive answer is “6.5”, which is probably the only reply that would render us a correct answer in the school’s math classes. But if we were to take the challenge from another perspective, the answer is not as obvious.

See if you can come up with more solutions. Think for a while and then scroll down towards the end of the page to see additionally four possible solutions.


By halving 13 expressed as Arabic or Roman numerals or letters, half of 12 may also be:

13    ⇒     1 and 3

XIII = XI and II   ⇒     11 and 2

Thirteen = Thir and teen   ⇒     4 and 4

XIII =    XIII        ⇒     VIII = 8    (upper part of the half)

Albert Einstein once said: “Most people stop looking when they find the proverbial needle in the haystack. I would continue looking to see if there were other needles.

svensk_flagga Detta blogginlägg på svenska

Author: Karl Ekdahl

International public health leader and creativity blogger.

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