Many of us are devoted to our morning crossword, acrostic, anagram or Sudoku puzzle. Quite a few religiously listen to the Sunday Puzzlemaster Will Shortz (who also sets puzzles for the New York Times) on National Public Radio.
So perhaps it is not surprising – even though many of us did not like school maths – that every so often a logical puzzle or maths problem goes viral. The most recent example is “Cheryl’s birthday”.
The puzzle was originally posted on the Facebook page of Singapore media personality Kenneth Hong, who said it was causing some debate with his wife.
Albert and Bernard just became friends with Cheryl. and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates.
May 15 May 16 May 19 June 17 June 18 July 14 July 16 August 14 August 15 August 17
Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.
Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too.
Bernard: At first I don’t know when Cheryl’s birthday is, but I know now.
Albert: Then I also know when Cheryl’s birthday is.
So when is Cheryl’s birthday?
Many people have tried their hand at solving the puzzle, including mathematician and writer Alex Bellos. Alex runs through it line by line, showing how he gets to the solution: the key is to ask what each of Bernard and Albert learn from the other’s statements.
Knowing what information is superfluous is often helpful, explains Alex:
The only way that Bernard could know the date with a single number, however, would be if Cheryl had told him 18 or 19, since of the ten date options only these numbers appear once, as May 19 and June 18.
Proceeding in like fashion (read the rest of Alex’s explanation here) we are led to:
The answer, therefore is July 16.
It has been suggested that it would have been easier to consult Cheryl’s Facebook page!
Where did Cheryl’s birthday problem arise?
The problem was set as a hard question on a regional competition for bright high school students: the Singapore and Asian Schools Math Olympiad (SASMO).
There is another in Australasia, and they culminate in the annual International Mathematical Olympiad, with the questions getting progressively harder as the regions grow. The world champion Maths Olympians (or “mathletes”) are incredibly gifted young problem solvers.
Cheryl’s birthday problem was inadvertently originally described as a grade 5 question for ordinary school kids in Singapore. This probably helped it go viral.
But why do certain things go viral in the first place? By convenient coincidence a new scientific study on The Secret to Online Success: What Makes Content Go Viral has just appeared – as described this week in Scientific American.
The researchers looked at what it was that made certain things “spread like wildfire” and whether it was possible to deliberately make content that would make something achieve viral status.
They found there were a number of things that could increase the chances of any content being widely shared.
Make it emotional – ideally triggering emotions like anger, anxiety or awe that tend to make our hearts race; and if you can, make it positive. This may be more even effective than other methods that are currently in wide use like targeting “influentials,” or opinion leaders. Crafting contagious content, as this research suggests, may provide more bang for your buck and create more reliably viral content.
You can tick off the emotional positives that helped Cheryl’s birthday problem go viral. It was unlikely and curious, but reassuring and nonthreatening. It did not tell you you were a dummy if you could not figure it out, far from it! A media personality helped it get going, and so on.
You can also inoculate against things going viral. My own worst-read blog in the Conversation had the unappetising title Danger of death: are we programmed to miscalculate risk?. This seemed to be bringing only bad news when in fact we discussed how to calculate relative risk better and be less alarmed.
A software company I helped set up 20 years ago saw the sales of one product sky-rocket when the name was changed from MathProbe (too medical?) to the more inviting Let’s do Math.
What makes a puzzle easy or hard
Cultural differences matter. For many years students in the French South Pacific were given exactly the same mathematics exams as those in Paris or Bordeaux.
A famous question asked students to “consider a dairy cow looking at the pole star on a snowy night”. This was served up for kids in the French South Pacific who in a far-ago pre-internet world had never seen snow, the northern sky, or even a cow.
Likewise numeric puzzles, such as Sudoku or nonograms, often arise in Japan or Korea whose ideogram based scripts make crosswords and anagrams a non-starter.
Keith Devlin, a mathematician who is a very gifted expositor, has a book The Math Instinct in which, among other things he describes how a change in language can make a seeming impervious problem easy.
For example, doing arithmetic in bases other than base ten sounds formidable. But whenever you watch a 50-50 cricket match and read on the screen that it is over 42.3, the ‘42’ are in base ten and the ‘3’ is in base six. Easy-peasy?
Similarly, you might discover that an abstract problem about probability can be expressed in terms of horse races or lotteries, or something else you know lots about.
Some other problems that went viral (or should have)
Conditional, sometimes counter-factual, thinking of the kind needed to determine Cheryl’s birthday is not something most humans find easy. Though there is a large subset of humanity who find some or all puzzles both enticing and accessible.
I had a friend who could usually do the notoriously hard cryptic crossword in the London Times in about ten minutes. He could not really explain how, he just saw the answers. I have another friend who is an expert crossword puzzle setter, as of course is Will Shortz.
Setting good puzzles or just good maths exam questions is an art in itself.
One of the most popular viral puzzles is known as the Monty Hall or “three door problem”. It has already been explained in The Conversation and makes a surprising story. It first went viral in large part because the correct answer seemed so unintuitive even to professional logicians.
To those who want to follow up on some other mind tickling examples I conclude with: