Due Date: Friday, Nov. 10, 2017, 23:55
See the General Guidelines for homework assignments.
This assignment must be done individually.
Here are the problems for Homework 9.
- A number of bacteria were placed in a Petri dish
at 10:00 am. One second later, each bacterium
reproduces by dividing into two bacteria, each as
large as the original bacterium was to begin with.
At 10:01 am (on the same morning), the Petri dish
becomes full. At what time was the Petri dish
half-full? Why?
-
A total of 101 spur gears are placed in a closed
chain, so that each gear meshes with exactly two
others:
Is it possible for all the gears to rotate simultaneously? Why or why not? - Fifteen boys gathered a total of 100 nuts. Is it
possible that no two boys gathered the same number
of nuts? Why or why not?
- You have two
explosive fuses of different lengths and a box of matches.
You know the following facts about the fuses:
- The fuses are not the same length.
- Each fuse will burn up in exactly 60 minutes.
- Each fuse burns at random rates. Thus
burning half a fuse may take less or more than
30 minutes.
-
A salesperson learned that the town's butcher needed
to buy a scale to weigh meats from 1 to 40 pounds.
The salesperson convinced the butcher that he could
save him a lot of money. He would sell the butcher
the double pan beam balance and the 4 weights below
at a big discount and that it would fully satisfy
the butcher's needs.
The butcher bought the scale and weights. Did he get taken? Is it really possible to weigh all integer increments from 1-40 using only 4 weights? Justify your answer.