Brain Teasers/Weighing the Tea into 2-lb Packets
A grocer proposed to put up 20 lbs of tea into 2-lb packets, but his weights had been misplaced by somebody and he could only find the 5-lb and the 9-lb weights. What is the quickest way for him to do the business?
- Put 20 lbs of tea one side, put 18 pound weights the other side. Remove 2 lbs of tea.
- Put the 2 lbs of tea back, and remove 2 lbs of tea out of 18 pound tea.
- Repeat this until 20 lbs tea is separated into 10 2 lbs portions.
This requires weighting 9 times.
- Put 9 lb weight one side, put 5 lb weight the other side.
- Add 4 lb of tea where the 5 lb weight is on.
- Remove the 4 lb tea, and weight another 4 lb tea
- After weighing 4 times, we get 5 4 lbs portions.
- Remove weights, split 4 lb tea until both sides are equal. Now we get 2 2 lbs tea.
- Repeat this with each 4 lb tea.
This requires weighting 9 times (4 + 5)