The Number Devil

The Number Devil by Hans Magnus Enzensberger Nights 1-3

Night 1 1. Who is the main character in the mathematical adventure? 2. What is the sequence of the combination lock referred to in the dream? 3. Describe the number devil. 4. What problem does the number devil present to Robert during their first encounter? Find the solution to this problem. 5. What are most genuine mathematicians bad at? 6. What does Robert liken to homework in his dream? 7. What makes numbers so devilish? What do you need to prove it? 8. How many numbers are there? How does the number devil describe large and small numbers? 9. Describe the pattern that occurs when squaring consecutive ones? Ex. 111² = 111 x 111 10. What is not allowed in mathematics? Why?

Night 2 1. What type of forest did Robert land in? 2. What was the last number to be discovered? Describe it. 3. What did the tiny flylike numbers represent? What digit was missing? 4. What was the problem with the Romans numbers? 5. When Robert writes 9 + 1 = 10, the number devil says, “One and zero? One plus zero doesn’t equal ten.” Why does the number devil make this assertion? 6. How can you make numbers hop? This is similar to writing numbers in what form? 7. How can you tell a number’s value? 8. What does the number devil mean by produce the number? 9. Robert wrote the year he was born in which two mathematical forms? 10. According to the number devil, what kinds of numbers exist?

Night 3 1. Why did Robert look forward to dreaming of the number devil? 2. Why didn’t Robert like division? 3. According to the number devil, dividing by what number is strictly forbidden? 4. What can only be divided by one and itself? 5. What is the mathematical term for what the book describes as prima donna numbers? List the first 15 prima-donna numbers. 6. Why weren’t the numbers 0 and 1 included in the number devil’s chart? 7. What must you do to a number to determine if it’s a prima donna? 8. What is the only even prima donna? 9. What does the number devil mean when he says, “Take any even number and I can find two prima donnas that add up to it.”? 10. How can you write the sum of an odd number greater than 5 using prima donna numbers? The Number Devil by Hans Magnus Enzensberger Nights 4-6

Night 4 1. How are 1÷3 and 1 similar? Find the result of this calculation. 3 2. The number devil states, “Fractions are something you can’t abide.” What does he mean? 3. If ⅓ of 33 bakers can make 89 pretzels in 2½ hours, then how many pretzels can 5¾ bakers make in 1½ hours? Find the discrepancy in this problem. 4. The number devil says, “The chain of nines behind the zero, if it goes on forever, will turn out to be equal to one.” What does he mean? Is this possible? If so, when? If not, why? 5. Why are the unreasonable numbers referred to as unreasonable? Identify the mathematical term for the unreasonable numbers. 6. How are hopping numbers and taking the rutabaga of numbers related? Find the rutabaga of 36. 7. Identify the mathematical term for taking the rutabaga of a number. What type of number is the rutabaga of two? 8. What is special about the number of small boxes within the squares drawn by the number devil? 9. How can you go from hopping numbers to taking the rutabaga of numbers using square models? 10. What is the relationship between the diagonal of a square and the sides of that square?

Night 5 1. According to the number devil, what is more exciting than numbers? 2. When Robert threw the coconuts to the ground, what shape did they form? 3. Describe the pattern made by the coconuts. How can the next number in the sequence (pattern) be determined? 4. Find 89 using the sum or two or three triangular numbers. 5. What type of number do you get if you add consecutive triangular numbers? 6. How does the number devil prove that 78 is the sum of the first 12 ordinary numbers? 7. What is the sum of the first 8 ordinary numbers? Explain your response. 8. What shape do you think quadrangle numbers form? Explain your response. 9. If you divide the squares and add the numbers, what is the most efficient strategy for adding the numbers? 10. What shapes do pentagonal and hexagonal numbers form? Identify the number of sides on each of these shapes.

Night 6

1. ‘Rn equals hn factorial times f of n open bracket a plus theta close bracket.’ Translate to mathematical symbols. 2. Which number begins the Bonacci numbers? Identify the mathematical term that refers to the Bonacci numbers. 3. How are the terms in the Fibonacci sequence generated? 4. The number devil ran through the Bonacci numbers in a singsong. Identify the error. 5. List 3 ways to generate other Bonacci numbers. Provide an example to justify your response. 6. Using the special rabbit clock, how long does a month last in the potato field? 7. How can you calculate the number of rabbits born without counting the rabbits? 8. What type of data display is used to show the rabbit problem? 9. Solve the tree problem on page 122. 10. List at least two places in nature where Bonacci numbers appear. The Number Devil by Hans Magnus Enzensberger Nights 7-9

Night 7 1. List three things in nature that understand how numbers work. 2. How many cubes were used to make the base of the pyramid built by Robert and the number devil? 3. Why does Robert tell the number devil, “It’ll never be a pyramid.”? 4. Which number does the triangle of numbers begin with? 5. How are the values for each cube calculated? 6. If you calculate the sum of each row, which type of numbers do you get? 7. Identify the numbers revealed along the diagonals of the multicolored triangle. 8. What happens when the number devil turns off the odd numbered cubes? Describe the diagram. 9. Compare and contrast the diagram with multiples of 2 and the diagram with multiples of 5. 10. Using the diagram on page 146, predict what the triangle will look like with multiples of 4 highlighted.

Night 8 1. How many possibilities are there of seating arrangements for two students? Three students? Four students? 2. How do you read the exclamation point in a mathematics problem? 3. What is the mathematical term for vroom? 4. If each of 5 students shook hands with another student before leaving, how many handshakes would occur? 5. Identify at least two ways to solve the handshake problem without counting each handshake. 6. What type of data display is used to show the number of group consisting of 3 students? 7. If there are 11 students in the broom brigade, how many groups consisting of 3 students exist? What is the mathematical term used to refer to the broom brigade? 8. How many groups would there be if 8 people volunteered for the broom-brigade quartet? 9. Use the number triangle to determine the number of groups there would be if there were 6 people volunteering for the broom-brigade duo. 10. If you have 14 volunteers taken 9 at a time, how many groups do you have?

Night 9 1. Which sets of numbers are represented by the first row? Second row? 2. How many red-shirted numbers are there compared to white-shirted numbers? 3. Which sets of numbers are represented by the third, fourth, fifth, sixth and seventh rows? 4. What are series? 5. What did the number devil write on the ceiling of Robert’s room? 6. How does the number devil use a model to show the series? 7. The first two numbers of the series written on the ceiling were 1 + 1. Find the sum. 2 3 8. Taking the next four terms in the series and adding them together, predict what the sum will be. What computation strategy was used to predict the answer? 9. Did they find an exact answer for the sum of groups of terms in the series? Why or why not? 10. Why did the number devil group the terms in the series the way he did? The Number Devil by Hans Magnus Enzensberger Nights 10-12

Night 10 1. How many sides or points did the snowflakes have? What geometric shape do they resemble? 2. How is the computer that Robert refers to in his dream similar to the technology used in your mathematics class? 3. Which number do all of the numbers “wobble” around? Identify the mathematical term for this number. 4. Take 1.618033989. Subtract 0.5. Double the result. Square the new result. What is the final result? 5. Based upon the reading, does the final result make sense? Explain your reasoning. 6. What is the mathematical term for a point where lines cross or come together? 7. Use the figures on page 203 to prove the formula true. Hint: White spaces are closed shapes. What types of figures does this formula work for? 8. Identify the figures that result from folding the nets on pages 204-205. 9. Dots plus spaces minus lines equals two. Translate to mathematical symbols. What types of figures does this formula work for? 10. Predict the answer to the question at the bottom of page 209.

Night 11 1. What does Robert want to know? 2. How does Robert “call out” the number devil? 3. What is another way to express 2x2x2? 4. What is the answer for any number to the 0 power? 5. What is another word for “a new idea”, in chapter 11? 6. What does a proof consist of? 7. Every ordinary number is followed by one number, what is that number? 8. Why can’t a “point” be divided? 9. How can two points on an even plain be connected? 10. How many possible routes are there to travel for two points connected by a straight line?

Night 12 1. Who came up with the word mathematics? 2. How many number devils were there? 3. What was Robert amazed by? 4. What is the Palace policy? 5. According to the number devil, who invented zero? 6. Why do number devils eat pies? 7. What is Robert’s title? What secret order does he belong to? What was hung around his neck? 8. What is the emblem of the secret order? 9. Solve the problem that Mr. Bockel presented to the class on page 251. Explain the process. 10. Is there a more efficient strategy that could’ve been used to solve the problem on page 251? If so, describe it.