Figure for Exercise 1
4
9
2.
Counting squares.
A square checkerboard is made up of
36 alternately colored 1 inch by 1 inch squares.
a)
What is the total number of squares that are visible on
this checkerboard? (
Hint:
Count the 6 by 6 squares,
then the 5 by 5 squares, and so on.)
b)
How many squares are visible on a checkerboard that
has 64 alternately colored 1 inch by 1 inch squares?
3.
Four fours.
Check out these equations:
4
4
4
4
1,
4
4
4
4
2,
4
4
4
4
3.
a)
Using exactly four 4’s write arithmetic expressions
whose values are 4, 5, 6, and so on. How far can you go?
b)
Repeat this exercise using four 5’s, three 4’s, and
three 5’s.
4.Four coins.Place four coins on a table with heads facingdownward. On each move you must turn over exactly threecoins. Count the number of moves it takes to get all fourcoins with heads facing upward. What is the minimumnumber of moves necessary to get all four heads facingupward?
6.
Hungry bugs.
If it takes a colony of termites one day to
devour a block of wood that is 2 inches wide, 2 inches
long, and 2 inches high, then how long will it take them
to devour a block of wood that is 4 inches wide, 4 inches
long, and 4 inches high? Assume that they keep eating
at the same rate.
7.
Ancient history.
This problem is from the second century.
Four numbers have a sum of 9900. The second exceeds the
first by one-seventh of the first. The third exceeds the sum
of the first two by 300. The fourth exceeds the sum of the
first three by 300. Find the four numbers.
8.
Related digits.
What is the largest four-digit number such
that the second digit is one-fourth of the third digit, the
third digit is twice the first digit, and the last digit is the
same as the first digit?
Photo for Exercise 5

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- Fall '12
- Withers
- Algebra, Exponents, Nonnegative Integral Exponents