Answers 245maining distance to Pig town, so it is clear that from Boghooley to Pigtown
took one hour.
Five miles beyond Pigtown we were at a point half as far from Ballyfoyne
as from Pigtown. Then we reached Ballyfoyne in an hour, from which we know
that we took 3 hours from Pigtown to Ballyfoyne, and therefore the time of
the complete journey was four hours. Now we find that the 5-mile run took
2 hours, so in the 4 hours we must have done 10 miles, which is the correct
distance from Boghooley to Ballyfoyne.
- A WALKING PROBLEM
The second man, on seeing his friend turn and walk towards him, walked
backwards 200 yards. It was an eccentric thing to do, but he did it, and it is
the only answer to the puzzle. They could thus have their faces towards each
other and be going in a direct line.- THE FALSE SCALES
If the scales had been false on account of the pans being unequally weighted,
then the true weight of the pudding would be 154 oz., and it would have
weighed 130 oz. in one pan and 178 oz. the other. Half the sum of the apparent
weights (the arithmetic mean) equals 154. But the illustration showed that the
pans weighed evenly and that the error was in the unequal lengths of the arms
of the balance. Therefore, the apparent weights were 121 oz. and 169 oz., and
the real weight 143 oz. Multiply the apparent weights together and we get the
square of 143-the geometric mean. The lengths of the arms were in the ratio
II to 13.
If we call the true weight x in each case, then we get the equations:
(-iTx + 4) + (-iTx + 52) = x, and x = 154.
2j({lX + 4) X ({IX + 52) = x, and x = 143.
- WEIGHING THE GOODS
Since one canister weighs an ounce, the first illustration shows that in one