Solution to Problem # 7

Here is our starting crosstable, before we've added any details.

Now let's proceed one step at a time:

1. We're given the following specific results: Ann beat Bill (clue #2), Chris beat Bill (clue #5) and the game between Dan and Bill was a draw (clue #7). With this data, our crosstable now looks like this:

2. Clue #2 tells us that Ann's only win came against Bill, so we know that Dan either drew with Ann or defeated her. We also know from clue #4 that Dan lost exactly two games. Since the crosstable already shows Dan's game with Bill ending in a tie, his only remaining games, with Chris and Ed, must be losses.

3. Clue #3 informs us that Ed scored two points total. Incorporating all of this new data, we now have the following crosstable:

4. Clue #1 tells us that Ed had the same result against Ann as he did against Chris. We know already that his game against Ann must have been a draw or a win. But if his game against Ann was a win, then from clue #1 this would mean he also defeated Chris. But this would give him a total of at least 3 points and we know (from clue #3) that he only scored 2 points total. Therefore, his games against Ann and Chris must both have been draws. This also means that Ed must have lost to Bill in order for Ed to total 2 points for the tournament. Now our crosstable looks like this:

5. We're almost done now. Clue #8 tells us that Bill had the same result against Ed as Dan did against Ann. Since Bill defeated Ed, this means that Dan also won against Ann. The last bit of information we need comes from clue #6, that at least four games were drawn. Since we only show three draws so far, the remaining game (Ann vs. Chris) must have been a draw. We can now complete our crosstable:

So Chris won the tournament with 3 points, Ann and Ed tied with 2 each, and Bill and Dan brought up the rear with 1.5 points each.

Now honestly, wasn't that fun?