So I asked her how she'd start. She started the way I'd want her to, by excluding the digits 2, 4, 5, 6, and 8 from the units place. And then...

...we got nuthin'.

What did the teacher want? Could we use the computer to test answers? Did the teacher teach some tricks I don't know about? Maybe.

After trying and failing to construct a few nine-digit nearly pandigital prime numbers, I finally gave into every programmer's temptation.

The brute-force tactic! Test them all! In Python, it looks like this:

#!usr/bin/python import itertools l = '123456789' for p in itertools.permutations( l ): n = int( ''.join(p) ) if isprime( n ): # find an implementation on the web print "Found it!", n break

We ran it and... What the hey‽ There

*isn't*any such prime‽ What kind of stunt is this teacher trying to pull?

pastillaJanuary 12 2012, 15:00:45 UTC 8 years ago

Did the teacher introduce a method or "trick" to the students beforehand . . . i.e. were the students exposed to any ideas that might encourage them to add all the digits up to see if they are divisible by anything?

The last two paragraphs explain (well, at least summarize) why you can't get a prime number out of these digits, and teaches a method.

My guess is that teaching the shortcut first will provide a foundation for understanding more complex factoring later.

If the teacher didn't teach this beforehand, and was trying to make a point through exhausting the kids . . . weak pedagogy, IMO!

sjonsvensonJanuary 12 2012, 22:23:57 UTC 8 years ago

tpedersonJanuary 25 2012, 03:45:43 UTC 8 years ago

45 is divisible by 3

dblumeJanuary 25 2012, 05:13:28 UTC 8 years ago