(Almost) Everybody hates deliberately ambiguous puzzles

You might have seen these puzzles, which have been doing the rounds on social media recently. What do you think the answers are?

Ambiguous fruit puzzle

a) 15. A bunch of bananas is a bunch of bananas. Who knows how many there really are in each one?
b) 14. There are four bananas in the bunches in lines 2 and 3, sort of, and there are only three bananas in the bunch in line 4.
c) 11. Nobody cares about boring old ordinary bananas. The only reason the bunches in lines 2 and 3 have any value is because of that special double-tipped banana. Without it, the rest of the bunch is worth zero.

Ambiguous flower puzzle

a) 26. A blue flower is a blue flower, regardless of how many leaves it has. A rose by any other name would smell as sweet.
b) 25. The flower head and stems are distractions, this is really about leaves.
c) The answer is undefined as there is no basis to say what the relationship is between the value of a blue flower with four leaves and one with five leaves. Consider how much more highly a four-leaf clover is regarded than a three-leaf one.

How many watermelons are there?

Ambiguous watermelon puzzle

a) Five. Three-quarters times four is three, and one-half times four is two.
b) Six. The middle four are two cut in half, the other four are used to produce the outer four. Yes, four quarter-melons are missing, but they clearly aren’t used to make up the ones in the middle.
c) An indeterminate number between six and eight, because we don’t can’t tell whether or not the ones in the middle are two halves of the same melon or not.
d) Zero. Three quarters of a melon and half a melon are both different things to a watermelon, notably in terms of freshness.

You might think that the fact that they’ve got hundreds of thousands of shares suggests they’re popular and thus worth including (or, at least, adapting) in your exit game. Please don’t. They’re popular because they’re deliberately ambiguous and can be argued more than one way. That’s really not a good property for an exit game puzzle. The fact that people are likely to have seen the puzzles, or their central conceits, before is not the best starting-point.

Counting puzzles have a long history in exit games and are a core skill. They’re hardly likely to excite, though there are a few cute ways to dress them up and if you have fantastic art then they can be genuinely pretty. The last time that a counting puzzle actually made someone smile was approximately 1898 (some reports suggest 1896) when Sam Loyd sold more than 10,000,000 copies of “Get Off The Earth” (discussed in detail, though the link is old and so the pictures have rotted, at the wonderful defective yeti) – and that’s perhaps better classed as an optical illusion than as a puzzle.

Algebraic equations are also known within exit games; if you write out the equations in words, then things are unambiguous. They may be a sufficiently close reminder of school that people who didn’t like algebra at the time are unlikely to appreciate the reminder now. The first puzzle of the three is the least problematic; if the bananas were completely separate from each other, it would be unambiguous, though not particularly exciting. As it is, it gets into issues of two-dimensional depictions of three-dimensional objects; why do you assume a banana is there when you can only see part of it, when you assume there isn’t any fruit hidden behind the apples?

One big problem with the puzzles above is that if you declare one of the answers to be correct and another to be wrong, then people are unlikely to be impressed by your explanation as to what makes something right or wrong. The bigger problem is that when people try what you consider to be the wrong answer and find out it doesn’t get them anywhere, they will probably stumble on the right answer by shifting one either way and then concluding that either their arithmetic was wrong (not much fun) or that your arithmetic was wrong (even less fun). It then becomes simple trial and error rather than puzzle-solving. It’s the sort of situation where only the person setting the room thinks it’s funny and the people playing the room think it’s not.

By contrast, if the “right” and “wrong” answers were, say, six away from each other and there were a satisfying reason why the “wrong” answer was wrong, that’s a much better puzzle – and whether a reason is satisfying or not is judged by the person hearing the answer, not the person setting the puzzle. This has been a very negative article so far, so here’s a constructive suggestion instead. If you’re effectively required not just to count up items for an equation but identify each item and work out whether thematically it fits into the category to be counted, that’s fine and potentially good; at worst, it’s a “how many animals of each time did Moses take into the ark?” trick question.

In short: stay well away from this sort of gimmick. The least worst thing that could be said about them is that they anchor the creation of your room to a particular point in time – specifically, this week or so – when everyone will have moved onto something completely different next week.

And as for the division sign in this little blighter, don’t even go there

Ambiguous division puzzle

Exit games in the media

Newspaper graphicHere’s a collection of stories of exit games making their impression on the public.

Crossword duel won by a knockout

ACPT 2015 final, care of the Visual Thesaurus YouTube channel

(thanks to the Visual Thesaurus YouTube channel)

Imagine, if you will, a crossword competition held at the TH_ND_RD_ME from Mad Max where two men may enter but one man must leave strictly positioned across and six feet down. Artistic licence is fun; the truth that led to the above genuine video still is, happily, far more prosaic.

The American Crossword Puzzle Tournament is the foremost competition of its type; a bold claim, made less contentious by a weaselly argument that the prestigious Times Crossword Championship here in the UK is a cryptic crossword competition and thus a slightly different type. Mark Goodliffe, eight-time Times champ and undefeated since 2007, as discussed in this brilliant article, has attended the US event in 2011 and 2013 and won transatlantic cryptic crosswords held there.

The ACPT has been running for nearly forty years; arguably, its high point was the release of the Wordplay film covering the 2005 championship; the attention drew the competition up from habitually drawing nearly 500 contestants to almost 700, though it has fallen back a little to 550 over the years. The 2000s started with four different winners in the millennium’s first five years; since then, Tyler Hinman established a dynasty by winning each year from 2005 to 2009, then Dan Feyer overtook him with a hegemony, winning each year from 2010 to 2014. 2015 would determine “first to six” between the pair, also noting Douglas Hoylman’s six wins over the years and Jon Delfin’s seven. Feyer winning a sixth consecutive event would also be a record.

This year’s event attracted more mainstream attention than usual, not least for its exciting conclusion that led to the photo above. Only a double handful or so of the hundreds of competitors solve all seven main-event puzzles completely correctly, including the legendarily difficult fifth puzzle, and the fastest three of them overall qualify for the overall championship. The second and third fastest suffer a time handicap penalty when solving the championship puzzle, starting this decisive puzzle a few seconds after the fastest solver of the main event. The first person to complete this puzzle, optionally check their answers, then signal their completion wins, if they have solved the puzzle correctly. As it’s a race, deciding whether or not to spend time checking your answers, and how much time to spend checking, is part of the challenge. This year, the video of the crucial three-quarter-second or so between Tyler and Dan finishing – but in what order? – demonstrates quite how big a part of the challenge it is, as shown below:

This year’s event, and its exciting conclusion, have drawn wider attention. Vocabulary.com have the times and more of the context; the awesome FiveThirtyEight have a brilliant longer piece on it as well, with more of the feel of the event and information on how a computer solver has done as a contestant over the years.

Anyone who has won the ACPT so many times is an outstanding solver. However, this site must declare an interest. One of the two blogs about topics including taking part in puzzle hunts and has tweeted about a trip over here featuring a win at Adventure Rooms in Dublin and 2/2 at Lock’d in London. More than enough reason for us to pick a favourite!

Cheryl and her birthday

Calendar with ten possible birthdays markedProbably this year’s most-talked-about logic puzzle concerns a birthday which is not explicitly revealed, but in that familiar fashion where just sufficiently many hints are given to reveal the information if you think about the clues and their implications.

The puzzle’s Singaporean origin is much discussed, generally making glowing and reverent reference to the nation’s world-renowned education system; at first, the puzzle was claimed to be a question asked of 11-year-olds, but a Singaporean site provides photographic evidence that it’s question 24 out of 25 (and, traditionally, the hardest questions are at the end) of a Singapore and Asian Schools Math Olympiad paper. This is aimed at the top 40% or so of students aged 14 or 15. Does that make you feel less bad about it? Not so much here, either…

The Guardian newspaper reports on the question and inspires over four thousand comments in the answers. They kindly follow up by posting a worked solution. A second answer proves popular in the comments and another post at the Guardian, two days later, argues in its favour.

If you’re curious, the answer I came up with was the second one, but I was convinced by the argument that the first one proves correct. For the argument from the definitive source, see the executive director of the contest’s clarification. Good enough for me; I was wrong.

Other than that, it’s interesting to see the world report on the reporting, as this post does once all the hoo-ha has died down. This site enjoyed the take at ronald.gl with a cute tale at the bottom and also coverage at the aperiodical which is the most comprehensive of the lot, not only with links to discussions in favour of the various arguments, many with videos, but also with links to several other puzzles at a variety of levels of formality and difficulty if you want to explore the field in further detail.

If this leaves you in the mood for more puzzles, the Escape Reviewer site of the Greater Toronto Area is running a contest starting at noon Eastern time (5pm UK time) today, in collaboration with Escape Games Review and Escape Room Addict who produced a puzzle hunt between them last month. There are scores of exit game prizes of interest to people nearby, but the puzzles should entice solvers worldwide. The previous puzzle hunt’s solutions are a work of art and feature ringing endorsements from known puzzle hunt veterans, though when they say “not too hard” there perhaps needs to be some… context applied from who’s being quoted.

Anyway, this leaves the world looking forward to this contest; as all the puzzles are being rolled out at once, rather than on a daily basis, perhaps that’s something to keep the world occupied this weekend!