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Three people are lined up behind each other, from shortest to tallest. They are shown five hats, three blues and two red. The people are blindfolded and were placed on their heads. The two extra hats were kept and the blindfolds were removed. All of them were asked if they knew what hat they were wearing, starting from the tallest. The tallest and the middle person both answered that he knows. How did he know and what color is the hat he is wearing? If 8 workers can finish a job in 6 hours, how many workers will it take to finish the same job in 4 hours? Find the unit digit for the sum 1325 + 481 +5411

Three people are lined up behind each other, from shortest to tallest. They are shown five hats, three blues and two red. The people are blindfolded and were placed on their heads. The two extra hats were kept and the blindfolds were removed. All of them were asked if they knew what hat they were wearing, starting from the tallest. The tallest and the middle person both answered that he knows. How did he know and what color is the hat he is wearing? If 8 workers can finish a job in 6 hours, how many workers will it take to finish the same job in 4 hours? Find the unit digit for the sum 1325 + 481 +5411

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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CHAPTER 3: PROBLEM SOLVING AND REASONING PROBLEM SET 1. Three people are lined up behind each other, from shortest to tallest. They are shown five hats, three blues and two red. The people are blindfolded and were placed on their heads. The two extra hats were kept and the blindfolds were removed. All of them were asked if they knew what hat they were wearing, starting from the tallest. The tallest and the middle person both answered that he knows. How did he know and what color is the hat he is wearing? 2. If 8 workers can finish a job in 6 hours, how many workers will it take to finish the same job in 4 hours? 3. Find the unit digit for the sum 1325 + 481 +5411. 4. An egg vendor broke all the eggs that he was delivering to a local store. He could not remember how many eggs there were in all. However, he did remember that when he tried to pack them into packages of 2, 3, 4, 5, and 6 he had one left over each time. When he packed them into packages of 7, he had none left over. What is the smallest number of eggs he could have had in the shipment? 5. There are 1000 lockers in a high school with 1000 students. The first student opens all 1000 lockers; next, the second student closes lockers 2, 4, 6, 8, 10, and so on up to locker 1000; the third student changes the state (opens lockers that are closed, closes lockers that are open) of lockers 3, 6, 9, 12, 15, and so on; the fourth student changes the state of lockers 4, 8, 12, 16, and so on. This continues until every student has had a turn. How many lockers will be open at the end? 6. Solve the given Ken-ken Puzzle 16x 7+ 2- 65-49 12X 2+ 2÷
Transcribed Image Text:CHAPTER 3: PROBLEM SOLVING AND REASONING PROBLEM SET 1. Three people are lined up behind each other, from shortest to tallest. They are shown five hats, three blues and two red. The people are blindfolded and were placed on their heads. The two extra hats were kept and the blindfolds were removed. All of them were asked if they knew what hat they were wearing, starting from the tallest. The tallest and the middle person both answered that he knows. How did he know and what color is the hat he is wearing? 2. If 8 workers can finish a job in 6 hours, how many workers will it take to finish the same job in 4 hours? 3. Find the unit digit for the sum 1325 + 481 +5411. 4. An egg vendor broke all the eggs that he was delivering to a local store. He could not remember how many eggs there were in all. However, he did remember that when he tried to pack them into packages of 2, 3, 4, 5, and 6 he had one left over each time. When he packed them into packages of 7, he had none left over. What is the smallest number of eggs he could have had in the shipment? 5. There are 1000 lockers in a high school with 1000 students. The first student opens all 1000 lockers; next, the second student closes lockers 2, 4, 6, 8, 10, and so on up to locker 1000; the third student changes the state (opens lockers that are closed, closes lockers that are open) of lockers 3, 6, 9, 12, 15, and so on; the fourth student changes the state of lockers 4, 8, 12, 16, and so on. This continues until every student has had a turn. How many lockers will be open at the end? 6. Solve the given Ken-ken Puzzle 16x 7+ 2- 65-49 12X 2+ 2÷
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