It is safer at backgammon to leave a blot in the tables which can be taken by an ace than one which a three would hit. In either the case of an actual ace or a three the chance is one in eleven; but there are two chances of throwing deuce-ace, the equivalent of three.
15.
If I start from a bay, where the needle points due north, 1200 miles from the North Pole, and the course is perfectly clear, I can never reach it if I steam continuously 20 miles an hour, steering always north by the compass needle. After about 200 miles I come upon the Magnetic Pole, which so affects the needle that it no longer leads me northward, and I may have to steer south by it to reach the geographical Pole.
16.
The 21 casks, 7 full, 7 half full, and 7 empty, were shared equally by A, B, and C, as follows:—
| Full cask. | Half full. | Empty. | |
|---|---|---|---|
| A | 2 | 3 | 2 |
| B | 2 | 3 | 2 |
| C | 3 | 1 | 3 |
| or— | |||
| A | 3 | 1 | 3 |
| B | 3 | 1 | 3 |
| C | 1 | 5 | 1 |
Thus each had 7 casks, and the equivalent of 31⁄2 caskfuls of wine.