Mathematics In the Modern World Assignment #3, Assignments of Mathematics

Download Mathematics In the Modern World Assignment #3 and more Assignments Mathematics in PDF only on Docsity! PROBLEM #1 1. In a class experiment, Miguel rolls one ordinary 6-sided die repeatedly. Keeping track of each number he rolls, he decides to stop as soon as one number is rolled three times. Miguel stops after the 12th roll, and the sum of these rolls is 47. Which number occurred for the third time? (An ordinary 6-sided die has the numbers from 1 through 6 on its sides) Step 1: Understand the Problem Find the number which occured for the 3rd time, if the sum of the 12th roll is 47. Step 2: Design a Plan We added all of the numbers that Miguel got in the die until we get the sum of the 12th roll which is 47. Step 3: Carry out the plan 6+3+5+4+6+1+3+5+4+3+1+6 = 47 6,6,6 rolled three times Step 4: Look back Miguel stops when number 6 rolled three times. 1st, 3rd and 12th roll got 6. PROBLEM #2 2. How many squares of all sizes are there on a standard 8-square by 8-square checkerboard? Step 1: Understand the problem Checkerboard size is 8 by 8 We need to find the number of squares on 8 x 8 checkerboard but the answer is not 64. Step 2: Design a plan n² = x n = square of all the numbers from 1-8. Step 3: Carry out the plan 8² x 7² x 6² x 5² x 4² x 3² x 2² x 1² 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 = 204 Total : 204 Step 4: Look back This is the sum of the number of possible positions for all the squares of size 1x1 to 8x8.