Mathematics of Modern World., Exercises of Mathematics

Download Mathematics of Modern World. and more Exercises Mathematics in PDF only on Docsity! Problem Solving & Reasoning Puzzles & Riddles 1. I am an odd number. Take away a letter and I become even. What number am I? Answer: SEVEN Conclusion: Using Polya’s Problem solving we can prove that the answer is SEVEN. a. Understand the problem: Odd number, take away a letter then becomes even. b. Devise a plan: Let’s assume numbers from (1-10). Let all the numbers change into word numbers, then find the odd numbers. c. Carry out the plan: From the odd numbers one, three, five & seven (1,3,5 & 7), find the word that can be change into the word even. d. Review the solution: Now we can see from the respective numbers that only the odd number (7) is suitable from the word SEVEN itself by taking away the letter “S” it will now become EVEN, therefore the answer is SEVEN. 2. Two fair coins are tossed simultaneously. In how many different chances It can have the two heads (2) and two tails (2)? Answer: Two heads have (1) chance & Two tails have chances (1). Conclusion: Using Polya’s Problem solving we can prove that the answer has one chances (1) for each, two heads and two tails. a. Understand the problem: There are many different orders by flipping two fair coins simultaneously, it could have two heads (HH) also it could also have two tails (TT) and of course there are other possibilities like a head and a tails (HT). b. Devise a plan: I’ll make a list of all possible orders and organized list to ensure that each of the different chances or possibilities will be listed once and once only. c. Carry out the plan: By tossing two fair coins simultaneously, we can see that there are 4 different chances shown below:  HH (Heads & Heads)  HT (Heads & Tails)  TH (Tails & Heads)  TT (Tails & Tails)