Earlier today I set you the following puzzle about the peculiar grammar of Yoda, Star Wars’ pointy-eared Jedi master.

Yoda inverts pairs of phrases before speaking. If Yoda says “Believe you I don’t”, we know what he means is “I don’t believe you.”

Here’s a way to mark up a Yoda sentence to recover its original meaning.

<[believe you] [I don’t]>

In this notation the “[ ]” means preserve the relative order of the phrases inside the brackets (of which there must be exactly two) and the “< >“ means invert the order. So in this case the annotation means “you” comes after “believe” and “don’t” comes after “I”, but “I don’t” comes before “believe you”.

**Puzzle Part I**

For each of these following annotated Yoda sentences, write down the original.

1) < go [ you must ] >

2) < [ strong [ with [ the force ] ] ] < [this [ one is ] ] < think I > > >

3) < [ < < home [ milk < coming before > ] > [ < to forget > < up pick > ] > tonight ] < don’t please > >

**Solutions**

1) You must go

2) I think this one is strong with the force

3) please don’t forget to pick up milk before coming home tonight

**Puzzle Part II**

Mark up the following Yoda sentences in such a way that they each recover the original meaning, which is ‘use the Force Luke’. It might be the case that there are multiple solutions (in which case say so) or there may be no solutions.

1) use Force Luke the

2) Luke the Force use

3) Luke Force the use

4) the Luke use Force

5) the Luke Force use

**Solutions**

1) [ Use < [ force Luke ] the > ]

2) < Luke < [ the force ] Use > > MORE POSSIBLE

3) < Luke < force < the Use > > > MORE POSSIBLE

4) NOT POSSIBLE

5) < [ the < Luke force > ] Use >

**Puzzle Part III**

There are 24 ways of ordering four objects. That’s because there are four choices for the first position, three choices left for the second position, two left for the third position, and one left for the fourth, making 4 x 3 x 2 x 1 = 24 possible choices.

If Yoda was able to rearrange the words ‘use the Force Luke’ in any way he wanted, therefore, there are 24 ways he could do this. *If he is only allowed to use the rules of this puzzle, that is using the [ ] and the < > brackets, how many ways are there that he can rearrange ‘use the Force Luke’?*

**Solution**

22

You could find this out by listing all 24 possibilities and getting stuck on two of them. Or you could notice the pattern from the previous part of the puzzle. If we number the words of “use the force Luke” as 1, 2 3 and 4, then 2413 fails, but the following are possible:

Add the notation:

[ 1 < [ 3 2 ] 4 > ]

< 4 < [ 2 3 ] 1 > >

< 4 < 3 < 2 1 > > >

< [ 2 < 4 3 > ] 1 >

In each case the two numbers that you must apply the bracket rule to first are adjacent numbers, meaning they are next to each other in the normal order of numbers. (In the first two they are 2 and 3, in the third 1 and 2, and in the fourth 3 and 4). Since the numbers are adjacent, the application of the rule will keep them adjacent, and they will stay adjacent on all subsequent applications of rules. Eventually, the rules produce a sequence of three numbers that are all adjacent and then finally four, which will get you a solution.

In other words, when you get two adjacent numbers a solution is possible.

However, look at 2413. It contains no sequence of two adjacent numbers, and this is why it is impossible to turn it into a sequence of four adjacent numbers. There are only two permutations of four digits which contain no adjacent numbers:

2413 and 3142.

So

the Luke use Force

Force use Luke the

are the only phrases that cannot pass Yoda’s mouth.

I hope you enjoyed today’s puzzle. I’ll be back in two weeks.

*I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.*

*Thanks again to Jonathan May, who wrote the puzzle, and to the North American Computational Linguistics Olympiad, where the puzzle originally appeared.*