## ________________

A bit of calculation and reasoning is always good exercise for the team.

## ________________

### The Size of Humanity

Two years ago, the Earth’s population reached 7.4 billion people. Consider the Earth as a sphere of radius 6,371 kilometers and spread the volume of humanity over the surface of the Earth in a shell of constant thickness. Assume the average person occupies a volume of 63,000 centimeters3.

How thick would the shell be?

### Fish Pond

A fish pond has a horizontal bottom and vertical sides. To make a platform, the owner places three identical, impermeable cubical blocks side by side, resting on the bottom. The first block causes a rise in water level of less than 12 inches. The second and third blocks each cause the level to rise exactly 12 inches.

How high in inches is the water level above the top of the completed platform?

## Solutions to week 129

In Circumnavigation, the circumference can be no more than 500 miles. In Typos, the number of expected typos is 5,040.

Both airplanes fly 100 miles toward one of the poles where airplane 2 tops off airplane 1 and returns to the island as its fuel is consumed. Airplane 1 continues over and beyond that pole, getting to within 100 miles from the island where its fuel is consumed. In the meantime, airplane 2 refuels at the island and takes off at the right time to just meet the incoming airplane 1 as it is running out of fuel. They divide the fuel from airplane 2 to just reach the island as their fuel runs out. The circumference can be no more than 500 miles.

Let the total number of typos be T. The first reader finds typos with a probability 252/T and the second reader finds them with a probability of 260/T. We are told that 13 typos were found by both so 13/T = (252/T)(260/T), from which we compute T = 5,040 typos.

## Recent Weeks

Links to all of the puzzles and solutions are on the Complete Varsity Math page.

Come back next week for answers and more puzzles.