Little explorations with HP calculators (no Prime)

[brickviking]

(12-26-2018 09:34 PM)pier4r Wrote:  The problem: there are 100 blue Christmas balls and 40 white Christmas balls in a line, randomly ordered. There are Anna and Berta that needs balls for their Christmas trees.

They decide that Anna will pick a continuous chunk of the line of length 70, for example between the position 3 and the position 72, the rest will be picked by Berta.

Could they find a way to ensure that Anna and Berta pick both 50 blue balls and 20 white balls? If yes, is a special arrangement of the balls needed to achieve it?

If a 'special arrangement of the balls" is necessary, wouldn't that mean that we couldn't in fact have a randomly ordered sequence after all? I contend (again, without a rigid mathematic proof, 'cos I'm not that bright) that you can't actually arrange the balls specially to 'guarantee' that both Anna and Bertha get their required proportions of Christmas baubles. In saying that, it does appear that in a very small number of sequences, you can actually get a clear run of 70 that matches the criteria, and thereby the remainder would also match the criteria, but only when glommed together into a line; but it's a fairly small percentage of chance.

(Post 324)