Figure for Exercise 1 4 9 2 Counting squares A square checkerboard is made up

Figure for exercise 1 4 9 2 counting squares a square

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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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