Maximum Lottery

Dr. Ecco Solution

Solution to "Election Fraud in Verity," DDJ, August 2005.

1. 1. There can be at most three pollsters meeting these conditions. Here's why. Each pollster must miss about 13 Wendy votes (because there are 51 in total, but only 38 seen by each pollster). No two pollsters miss the same Wendy voter, because every pair of pollsters interview all 100 voters. If we number the Wendy voters W1 to W51, then we can imagine that pollster A misses W1 to W13, pollster B misses W14 to W26, and pollster C misses W27 to W39. There are not enough more Wendy voters for a fourth pollster to miss, so there can be only three pollsters.
2. 2. Number the Fred voters F1 to F49. Pollster A could interview W14 to W51 and F1 to F42. Then pollster B could interview W1 to W13 and W27 to W51 as well as F8 to F49. Finally, pollster C could interview W1 to W16 and W40 to W51 as well as F1 to F7 and F15 to F49.
3. 3. As the solution to the first question showed, this result would not be possible with five honest pollsters. So Fred was right: Wendy stole the election.

Tom Rokicki helped enormously with these solutions.