HCI/UX-Related Logical Problem

In April 2016 I asked for participants to solve a logic puzzle. Here it is:

This is a different form of a known logic puzzle. If you recognize the puzzle, please tick the bottom answer! [The bottom answer is omitted here, but it was 'I recognize the puzzle']

There are three blocks stacked on top of each other. A is on the top, B is in the middle and C is on the bottom. Each is coloured on one face either red or blue. A is red and C is blue but we cannot see the coloured face of the middle block, B.

Is a red block directly on top of a blue block?

The answers offered were 'Yes', 'No' and 'Would have to know the colour of block B'. Of the 463 respondents who didn't recognize the puzzle (if they did, they would have already known the answer), the response counts were:

44.1% Yes
10.2% No
45.8% Would have to know the colour of block B

The correct answer was 'Yes', so most people got it wrong (44% vs 56% approximately).

Where the HCI/UX comes in is that a similar puzzle, using people and marriage, rather than blocks and colours, does even worse. Alex Bellos of The Guardian ran a similar puzzle on their web site in March. His results, with around 200,000 respondents, were

27.7% Yes
4.5% No
67.8% Cannot be determined

My theory was that because Anne (the logical equivalent of the block with the unknown colour) was a person, we were less likely to take an abstract route to solving the problem. As Alex points out, 'Anne’s marital status is irrelevant to the answer'. However, when I was looking at this problem for the first time, it never occurred to me that I could solve it with pure logic, even though I was in the middle of marking papers on propositional logic at the time.

I don't know a good way of comparing such vastly different group sizes (if anyone does, please write to me!) but if we just cheat and apply the marriage problem percentages to my block problem respondent count of 463, we get a statistically very significant result (p < 0.00001). However, it may be that self-selection is somewhat different between my respondents and Alex's or that the reworking of the problem changes more than intended.

Either way, I think it demonstrates again, that how we express problems can have a huge impact on how we think about them. In the marriage version of this logic puzzle, respondents seemed quite certain that the couldn't solve the problem without knowing Anne's marriage status. For UCD that is a good thing! (BTW, it was the Guardian readers who thought this, not my UCD/UX contacts.)

William Hudson (7 June 2016, Unpublished)

Other publications by William Hudson