[math-fun] Unsolved puzzle from Le Monde

First problem: in Alice's small city, 10 council members had to be elected. Each voter could vote for 10 candidates, out of a list of 25. What is the largest possible number of voters... [such that] every voter has at least one of the candidates he voted for elected in the council, no matter what...

First problem: 1358

One can show that 1358 voters can be satisfied, using a fairly obvious algorithm to choose the elected from the ballots. The problem is to rig 1359 ballots so that (at least) one voter must be left unsatisfied. Here's an easier (?) derived problem: there are 17 candidates; 2 will be chosen; and 8 voters, each voting for 10. (7 voters can be satisfied.) Can you rig 8 ballots? -- Don Reble djr@nk.ca