Not long ago, I had occasion to travel to Ottawa and back on *VIΛ* (which is the only Crown corporation I know of that's named after a preposition, and which spells its name with a lambda instead of an A presumably for the sake of rotational symmetry), so I had a look at the puzzles near the back of the February/March issue of Destinations, their earthbound equivalent of an in-flight magazine. Unlike some, I'm no puzzle expert,^{1} but I do have a couple of critical thoughts to share from my decidedly amateurish perspective.

**Spoiler alert:** If you are planning to ride a train in Canada before the end of this month (or whenever *VIΛ* gets around to distributing the next issue of Destinations), then reading the rest of this post **may deprive you of a few brief moments of mildly pleasant diversion** on your journey. **You may find yourself compelled to spend those minutes looking at the passing scenery instead.**^{2} You have been warned!

The puzzles I was interested in all involved finding the next item in a given sequence. Three of them were sequences of integers:

- 6-8-12-20- ?
- 2-6-14-30- ?
- 4-5-7-11-19- ?

Any one of these I would have found uninspired but tolerable by itself, but for them to print all three in the same issue just seemed silly. What do you think?

Another sequence involved pairs of integers and letters:

- 3:T, 6:S, 7:S, 9:N, 13: ?

This isn't very original, but eventually I realized that it's actually at least a little bit cleverer than it looks. You can make a more interesting puzzle out of it by asking for the next number–letter pair, rather than giving the number and asking which letter goes with it.

Here are *VIΛ*'s answers and explanations for the first set:

- 36 (–2 ×2)
- 62 (+1 ×2)
- 35 (×2 –3)

If you look at it like that, then each of them has a different method for obtaining the next number in the sequence, although each one involves multiplying by two. But I was solving these by looking at the differences between adjacent numbers (which is what I usually try first in puzzles like this), and in each one, you just keep adding the next power of two. So to me, this was essentially the same puzzle three times over, rather than three different puzzles—the numbers of the overt sequences sort of fade away into the background, and the powers of two between them stand out. (I'd be interested to hear if my readers had the same reaction, or if you see these sequences differently.)

In the second one, **T**hirteen maps, of course, to T. The next pair would have to be 16:S. The numbers given by *VIΛ* look like the beginning of this sequence, but the railway's choice of numbers had a linguistic basis rather than a mathematical one. The puzzle is bilingual, so the sequence of numbers is the ones that begin with the same letter in English and French:

3 6 7 9 13 16 30 ... three six seven nine thirteen sixteen thirty ... trois six sept neuf treize seize trente ...

(And they could have started off with 0:Z, but that might have been too obvious.)

This is, I think, a pretty neat exploitation of the similarity between Canada's two official languages.

1. My one tenuous basis for a claim of authority here is that I was once invited to co-edit a scholarly journal on enigmatology. I declined on the grounds that I was wholly unqualified.

2. If you encounter delays *en route,* you may even be compelled to watch **non-passing** scenery.