2009 April | Polymath Programmer

In-flight entertainment user interface … difficulty

April 3, 2009 By Vincent

I just returned to Singapore from Japan. It’s because of this that I found a fellow traveller’s experience of his in-flight entertainment system hilarious, both as a traveller and as a programmer. I wanted a stronger word than “difficulty” in the title (such as “hell”) but thought I’d tone it down to distract the dragonflies.

If you ever want to punish a user interface designer, make sure they get to use an airline’s long-haul inflight entertainment system. It must be like hell on earth for them.

My experience was a bit less distraught than James’. I flew on Singapore Airlines, the Airbus to Japan, normal plane back to Singapore. The entertainment system on the Airbus was good, and the one on the normal plane was ok. And I’m not just saying that because I’m Singaporean.

The only complaint I have is the seat was uncomfortable for me. The seats are not designed for tall people… My neck was sore for most of the flight. I’ll tell you more of my trip later.

The composite space between prime products

April 2, 2009 By Vincent

Previously, I gave you a puzzle on prime numbers.

Let F(n) be (1st prime) * (2nd prime) * … * (nth prime)
The question was to describe the group of numbers between 2 and F(n)-1 that F(n) cannot divide.

And the answer is… all composite numbers between 2 and F(n)-1 with repeated prime factors. Hmm… I guess that doesn’t quite fit the “as plain an English as possible”, but it is concise.

For example, F(n) cannot divide 4, because 4 = 2*2 (repeated 2).
But F(n) divides 6, because 6 = 2*3 (no repeated primes).
F(n) cannot divide 18, because 18 = 2*3*3 (repeated 3).

The proof (sort of)

If a number A in [ 2, F(n)-1 ), is prime, then F(n) divides A by definition because F(n) is a product of primes.

Let A be a composite number in [ 2, F(n)-1 ) with no repeated prime factors. Then F(n) divides A because F(n) is a product of primes where the prime factors form a superset of the prime factors of A.