I've reconstructed a puzzle which I remember being amused by when I came across it in a school textbook.
We expect that if you add a quantity to itself, and then take half of the result, you get the origal quantity. That doesn't happen here.
Background: Imperial measurements. One rod (or perch) is 5.5 yards. 1 chain is 4 perches or 22 yards. 1 furlong is 10 chains or 220 yards One mile is 8 furlongs or 1760 yards.
Now. let's start with a distance of 1 mile, 7 furlongs, 9 chains, 3 rods and 7 yards, Let's add this to itself.
1 7 9 3 7
+ 1 7 9 3 7
= 4 0 0 0 3 which when we divide by 2 gives
2 0 0 0 1.5
So the sum is four miles and 3 yards, and if we divide this by two, we get 2 miles 0 furlongs 0 chains 0 rods and 1.5 yards - not what we started with! Can you explain?
(The addition, in detail, from the right)
7 yards plus 7 yards is 14 yards which is 2 rods plus 3 yards,
3 rods plus 3 rods plus 2 rods (carried) is 8 rods which is 2 chains plus 0 rods,
9 chains + 9 chains plus 2 chains(carried) is 20 chains = 2 furlongs 0 chains,
7 furlongs + 7 furlongs plus 2 furlongs (carried) is 16 furlongs = 2 miles 0 furlongs
1 mile + 1 mile plus 2 miles (carried) is 4 miles.
