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Name _____________ADVANCED Tic-Tac-Toe Homework for the week of May 18, 2015 - DUE FRIDAY 1) A jar has exactly 10 blue marbles, 10 gray marbles, 10 red marbles, and 10 green marbles. If I cannot see the marbles, what is the fewest number of marbles I must pick without replacement in order to guarantee that three of the marbles I pick are red? 2) In this correct multiplication example, different letters represent different digits. What three-digit number is represented by SUM? You must show your work mathematically and explain your strategy. You must show your work mathematically and explain your strategy. 4) A path is traced from point A to point B by using the segments shown in the diagram at the right. Paths are traced only upwards, to the right, or diagonally upwards. How many different paths can be traced from A to B? 3) The symbol 3! Means 3x2x1, which equals 6. Similarly, 5! Means 5x4x3x2x1, which equals 120, and so on. Suppose N! ends in exactly 3 zeros after fully multiplying out. What is the smallest value that N can have? 5) In the multiplication example: ABxC=AAA, different letters represent different digits, AB represents a two-digit number, and AAA represents a three-digit number. What is the value of C? You must show your work mathematically and explain your strategy. 6) A hat contains 20 slips numbered consecutively from 71 to 90. Karen draws 10 slips from the hat including the “74”. Rob draws the other 10 slips including the “89.” Each adds the numbers written on his or her slips. What is the largest amount by which Karen’s total can be greater than Rob’s total? You must show your work mathematically and explain your strategy. 7) Both ABC and 3D8 are threedigit numbers such that ABC3D8=269. IF 3D8 is divisible by 9, what number does ABC represent? 8) Carol choses a number. She multiplies it by 4, then adds 8, then divides by 4, and finally subtracts 8. Her end result is 4. What number did she choose? You must show your work mathematically and explain your strategy. You must show your work mathematically and explain your strategy. 9) The large square shown contains smaller squares A, B, and C. Their areas are 9, 16, and 9 sq m respectively. How many sq m are in the area of the shaded region? 1) p. 87 2A set 13;2 I must pick 33 marbles in order to guarantee that 3 marbles are red 2) pg. 88 3C set 13;3 SUM represents 625 3) p. 82 2E, set 12;2 The least value of N is 15 4) p. 88 3E set 13;3 To reach point B from point A a total of 13 paths can be traced 5) p. 85, 5E, set 12; 5 The value of C is 9 6) p. 85, 5C, set 12; 5 Karen’s total is 70 more than Rob’s total 7)p. 84, 4D, set 12; 4 ABC is 647 8) p. 84, 4A, set 12, 4 Carol choses the number 10 9) p. 87, 2E set 13;2 The area of the shaded region is 42 square meters