Q: Which option is larger? No calculators please!

a) the sum of all cubes from 100 to 200

b) the sum of all squares from 1 to 100

squares are the numbers 1^2, 2^2 etc and cubes are 1^3, 2^3 etc

A: The squares.
The only cube from 100 to 200 is 125

But the squares from 1 to 100 include 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 = 385 so the sum of the squares is larger.

Q: There are two ducks in front of two ducks, two ducks behind two ducks and two ducks in between. What is the minimum number of ducks?

A: 4 ducks

The largest number is 140,625 = (5/1)^(6) * 3^(4/2)

h=4

A; There are 8 possible answers:
3 and 5,
3 and 6,
4 and 4,
4 and 5,
2 and 5,
2 and 6,
1 and 5,
1 and 6