You could describe me as a ‘puzzle enthusiast’. I look back fondly at the month I took out of my PhD to do a GCHQ Christmas Quiz (although I’m still annoyed that I didn’t win the darned paperweight). There is joy in discussing difficult problems with like-minded people, bonding whilst trying out different ideas and, hopefully, celebrating together when a solution is found.
Every morning Radio 4’s Today programme issues a Puzzle for Today. These usually take the form of a mathematical or logic puzzle and their difficulty varies substantially. An index of recent puzzles can be found here. Over the last few weeks there has been a discussion online criticising these puzzles. One supposedly poor puzzle was Puzzle No. 464, set on Tuesday 23 April 2019.
Puzzle No. 464
A drake, rook, duck and cuckoo are playing a personalised game of cards, but are arguing whether an ace is worth 1 or 11. The drake says his hand of cards are worth 8, the rook says hers are worth 4, the duck says her are worth 6, and the cuckoo says his are worth 3. What value should the ace be set at, to stop the birds being angry?
You can find the solution to Puzzle No. 464 further down this post.
Part of my job involves writing interesting puzzles for school students and I want to collect my thoughts on puzzles and puzzle-setting here. Let’s begin with a question I found here.
P: Chris came to a market to sell some eggs. Three people bought the eggs. The first buyer took half the eggs plus half an egg. The second buyer took half the remaining eggs plus half an egg. The third buyer bought what was left over: 1 egg. How many eggs were there initially?
You can find the answer to P at the bottom of this post. Suppose question P appeared in a maths text book, I would consider it just an algebra question. But, were P to appear in a newspaper, I would think of it as a puzzle. Context matters.
When setting a puzzle, I start with the audience. What prior knowledge can we safely assume of our audience? A cryptic crossword, for example is ill suited to six-year olds because a six-year-old is very unlikely to understand the methods need to solve the puzzle. I ask myself how able is the audience and what will challenge them?
I think about how much time I want the audience to spend finding the answer. I ask students to complete four puzzles during a one-hour lunch break which gives me a very clear target. A puzzle should always be both solvable and non-trivial. A lot of satisfaction comes from having solved a genuine problem and exerted some effort.
I always strive for clarity, both in the question and the answer. Puzzle-setters should be humble enough not to expect the audience to know what they are thinking. This is much more difficult skill than you might imagine! Trying to spot ambiguities in a puzzle requires empathy.
Here is the answer to Puzzle No. 464:
This is because the birds have assigned the values of their hands of cards to the sum of the letters in their names (after all, it is personalised), where each letter has its own numerical value. Fortunately we need not attempt to calculate the values of individual letters because, through cancelling the letters in their names, one can see that: Drake-duck-rook+cuckoo=ace. Using the given values, this means ace=8-6-4+3=1.
Puzzles that are just tricks, or jokes, or riddles often leave the reader feeling cheated or worse, stupid. This, I believe, is why Puzzle No. 464 frustrated some people. The fundamental problem with Puzzle No. 464 is that it isn’t suitable for the audience. It would be a great fit for a GCHQ quiz book where the riddles flow, but not for the majority of Radio 4 listeners.
Radio 4 should ensure that every Puzzle for Today is clear, solvable and have a single solution. They should also either steer away from riddles or pose a ‘Riddle for Today’.
The huge and varied audience of Today means that it is extremely hard for the problem setters to answer the big question: who is this puzzle for? They cannot easily assume a level of prior knowledge or a suitable difficulty, so perhaps we should cut them some slack.
Answer to puzzle P: