You can imagine an arrow in flight, toward a target. For the arrow to reach the target, the arrow must first travel half of the overall distance from the starting point to the target. Next, the arrow must travel half of the remaining distance.
For example, if the starting distance was 10m, the arrow first travels 5m, then 2.5m.
If you extend this concept further, you can imagine the resulting distances getting smaller and smaller. Will the arrow ever reach the target?
Hint
How many miles were left at the start of yesterday?
Answer
336 miles.
Reasoning
To work these numbers out, it is perhaps easier to start at the end and work backwards.
Yesterday I travelled 1/3 of the distance to leave 21 miles, therefore there were 31.5 miles (=21 ÷ 2/3) at the start of yesterday.
On day 3 I travelled 3/4 of the distance to leave 31.5 miles, therefore there were 126 miles (=31.5 ÷ 1/4) at the start of day 3.
On day 2 I travelled 1/2 of the distance to leave 126 miles, therefore there were 252 miles (=126 ÷ 1/2) at the start of day 2.
On day 1, I travelled 1/4 of the distance to leave 252 miles, therefore there were 336 miles (=252 ÷ 3/4) at the start of day 1.
Double-Checking
On day one, I travelled one quarter of the distance (84, leaving 252).
On day two, I travelled one half of the remaining distance (126, leaving 126).
On day three, I travelled three quarters of the remaining distance (94.5, leaving 31.5).
Yesterday I travelled one third of the remaining distance (10.5).
I now have 21 miles left to travel.
??
Puzzle 4
The BrainBashers Dictionary of Proverbs is running out of memory.
Below are four proverbs with their vowels missing and the remaining letters are grouped in fours.
dntb tthh ndth tfds y
trth wllt
bslw nchs ngbt slwr nchn gng
thnk frst ndth nspk
