Puzzle and meta-puzzle: Factorisation

(This was suggested to me by a friend.)

Find the prime factorisation of 12318876808768112319.

Factorisation puzzles are familiar, and obviously the point is to minimise the use of computer assistance, by making ‘clever’ observations.

Once you see how to do it, you’ll notice that there is a still a non-trivial amount of checking to do. Thus, a meta-puzzle suggests itself: to find a natural number N, so that the problem of factorising N by hand contains lots of interesting and clever observations, and very little checking.

I don’t know how to solve this meta-puzzle!


Puzzle: Cinema Trip

Three friends—Alsa, Bjorn, and Cally—want to go to the cinema.

There are five films:

  • Star Wars X,
  • Avengers Rereunite,
  • Frozen 3 – ice cold,
  • Fish and chips – the inside story,
  • Harry Potter and the Arithmancer of Andover.

There are three choices of snack:

  • Basil popcorn,
  • Chilli marshmallows,
  • Vegan burger.There are four choices of drink:
  • 8 down,
  • Diet Cake,
  • Popsi Minimum,
  • Ginger coffee.

They don’t mind going to separate films, but Cally won’t miss Star Wars if either of the others sees it (because she’s worried about spoilers). Each of them wants a drink of their own, and a snack of their own, except that the bags of marshmallows must be shared between two of them.

How many configurations of cinema trip may our three friends choose?