Math questions and answers
Muchos mangos. You inherit a large crate of mangos. The top layer has 21 mangos. Peering
through the cracks in the side of the crate, you estimate there are four layers of mangos
inside. About how many mangos did you inherit? - correct answer-21 x 4 = 84 mangos.
You have an empty CD rack consisting of 13 shelves and you just bought 13 totally kickin'
CDs. Can each CD go on a different shelf?
What if you had 14 new CDs? - correct answer-Yes; some shelf must have two CDs
Twenty-nine is fine. Find the most interesting property you can, unrelated to size, that the
number 29 has and that the number 27 does not have. - correct answer-Two possible
candidates: First, 29 is prime. Secondly, 29 happens to be the sum of three consecutive
squares, 29 = 4 + 9 + 16. Lest the number 27 feel left out, it should be noted that 27 =
3×3×3, a perfect cube. Is the set of prime numbers sparser than the set of perfect cubes?
Does this make it less interesting in your eyes?
Suppose you were able to take a large piece of paper of ordinary thickness and fold it in half
53 times. What would the height of the folded paper be? Would it be less than a foot? About
one yard? As long as a street block? As tall as the Empire State Building? Taller than Mount
Everest? (Assume that packages of 200 sheets of paper are more than half an inch thick.) -
correct answer-To get started, let us estimate the thickness of an ordinary piece of paper by
noting that packages of 200 sheets of paper are more than half an inch thick. So, a single
piece of paper is at least 1/400 inches thick. Now, after one folding, the paper is twice the
original thickness. After 2 foldings, the paper is 4 = 22 times as thick.
The height would be more than 23000000000000
inches. [Round your answer to 02 significant digits.]
After 53 foldings, the paper will be 0253 times as thick. The resulting paper is then 0253/400
inches thick. (That is about 2.3 × 1013 inches and about 355 million miles!)
Fifteen Fibonaccis. List the first 15 Fibonacci numbers. - correct answer-1, 1, 2, 3, 5, 8, 13,
21, 34, 55, 89, 144, 233, 377, 610
Born φ. What is the precise number that the symbol φ represents? What sequence of
numbers approaches φ? Choose all correct answers. - correct answer-The symbol φ
represents the infinitely long fractal expression / The symbol φ represents a solution to the
equation / A sequence of numbers that approaches φ is the list of ratios of consecutive
Fibonacci numbers.
This question gave the Fibonacci sequence its name. It was posed and answered by
Leonardo of Pisa, better known as Fibonacci. Suppose we have a pair of baby rabbits: one
male and one female. Let us assume that rabbits cannot reproduce until they are one month
old and that they have a one - month gestation period. Once they start reproducing, they
,produce a pair of bunnies each month (one of each sex). Assuming that no pair ever dies,
how many pairs of rabbits will exist in a particular month? During the first month, the bunnies
grow into rabbits. After two months, they are the proud parents of a pair of bunnies. There
will now be two pairs of rabbits: the original, mature pair and a new pair of bunnies. The next
month, the original pair produces another pair of bunnies, but the new pair of bunnies is
unable to reproduce until the following month. Thus we have:
Continue to fill in this chart and search for a pattern - correct answer-1, 1, 2, 3, 5, 8, 13, 21
Discovering Fibonacci relationships (S)
We'll use the symbol F1 to stand for the first Fibonacci number, F2 for the second Fibonacci
number, F3 for the third Fibonacci number, and so forth. So F1 = 1, and F2 = 1, and,
therefore, F3 = F2 + F1 = 2, and F4 = F3 + F2 = 3, and so on. In other words, we write Fn for
the nth Fibonacci number where n represents any natural number; for example, we denote
the 10th Fibonacci number as F10 and hence
we have F10 = 55. So, the rule for generating the next Fibonacci number by adding up the
previous two can now be stated, in general, symbolically as:
Fn = Fn − 1 + Fn − 2
By experimenting with numerous examples in search of a pattern, determine a simple
formula for (Fn +1)2 + (Fn)2; that is, a formula for the sum of the squares of two consecutive
Fibonacci numbers. - correct answer-(Fn +1)2 + (Fn)2 = F2n + 1 for n ≥ 01
Sum of Fibonacci (H). Express each of the following natural numbers as a sum of distinct,
nonconsecutive Fibonacci numbers: 356, 948, 610, 1289.
In each case, enter the Fibonacci numbers in descending numerical order: 356, 948, 610,
1289 - correct answer-356= 233, 89, 34
948= 610, 233, 89, 13, 3
610= 610
1289= 987, 233, 55, 13, 1
Sum of Fibonacci. Express the natural number 31 as a sum of distinct, nonconsecutive
Fibonacci numbers given in descending order (e.g. 55+21+3). - correct answer-21+8+2
Primal instincts. List the first 15 prime numbers. - correct answer-2, 3, 5, 7, 11, 13, 17, 19,
23, 29, 31, 37, 41, 43, 47
Fear factor. Express each of the following numbers as a product of primes: 77, 7889, 8, 39,
5643. - correct answer-77 = 7 x 11
7889 = 7 x 7 x 7 x 23
8=2x2x2
39 = 3 x 13
5643 = 3 x 3 x 3 x 11 x 19
, Odd couple. If n is an odd number greater than or equal to 3, can n + 01 ever be prime?
What if n equals 01? - correct answer-No. Then n + 01 is prime.
Always, sometimes, never. Does a prime multiplied by a prime ever result in a prime? Does
a nonprime multiplied by a nonprime ever result in a prime? Always? Sometimes? Never?
Explain your answers. - correct answer-Never, by definition.
Never, by definition.
Twin primes. Find the first 15 pairs of twin primes. - correct answer-(3,5), (5,7), (11,13),
(17,19), (29,31), (41,43), (59,61), (71,73), (101,103), (107,109), (137,139), (149,151),
(179,181), (191,193), (197,199)
Floating in factors. What is the smallest natural number that has three distinct prime factors
in its factorization? - correct answer-30
You own a very expensive watch that is currently flashing "7:15." What time will it read in 12
hours? In 17 hours? In 26 hours? In 336 hours? What time is it when an elephant sits on it? -
correct answer-In 12 hours it will read 7:15
In 17 hours it will read 12:15
In 26 hours it will read 9:15
In 336 hours it will read 7:15
Living in the past. Your watch currently reads "2:45." What time did it read in 24 hours
earlier? Three hours earlier? Thirty-one hours earlier? What time did it read 2400 hours
earlier? - correct answer-24 hours earlier it read 2:45
Three hours earlier it read 11:45
Thirty-one hours earlier it read 7:45
2400 hours earlier it read 2:45
Hours and hours. The clock now reads 10:45. What time will the clock read in 60 hours?
What time will the clock read in 860 hours?
Suppose the clock reads 07:30. What did the clock read 28 hours earlier?
What did the clock read 96 hours earlier? - correct answer-10:45
6:45
3:30
7:30
Celestial seasonings (S). Which of the following is the correct UPC for Celestial Seasonings
Ginseng Plus Herb Tea? Show why the other numbers are not valid UPCs. - correct
answer-Check sum for 0 70743 00021 8 = 42
Check sum for 0 70734 00021 8 = 40
Check sum for 0 71734 00021 8 = 43
Muchos mangos. You inherit a large crate of mangos. The top layer has 21 mangos. Peering
through the cracks in the side of the crate, you estimate there are four layers of mangos
inside. About how many mangos did you inherit? - correct answer-21 x 4 = 84 mangos.
You have an empty CD rack consisting of 13 shelves and you just bought 13 totally kickin'
CDs. Can each CD go on a different shelf?
What if you had 14 new CDs? - correct answer-Yes; some shelf must have two CDs
Twenty-nine is fine. Find the most interesting property you can, unrelated to size, that the
number 29 has and that the number 27 does not have. - correct answer-Two possible
candidates: First, 29 is prime. Secondly, 29 happens to be the sum of three consecutive
squares, 29 = 4 + 9 + 16. Lest the number 27 feel left out, it should be noted that 27 =
3×3×3, a perfect cube. Is the set of prime numbers sparser than the set of perfect cubes?
Does this make it less interesting in your eyes?
Suppose you were able to take a large piece of paper of ordinary thickness and fold it in half
53 times. What would the height of the folded paper be? Would it be less than a foot? About
one yard? As long as a street block? As tall as the Empire State Building? Taller than Mount
Everest? (Assume that packages of 200 sheets of paper are more than half an inch thick.) -
correct answer-To get started, let us estimate the thickness of an ordinary piece of paper by
noting that packages of 200 sheets of paper are more than half an inch thick. So, a single
piece of paper is at least 1/400 inches thick. Now, after one folding, the paper is twice the
original thickness. After 2 foldings, the paper is 4 = 22 times as thick.
The height would be more than 23000000000000
inches. [Round your answer to 02 significant digits.]
After 53 foldings, the paper will be 0253 times as thick. The resulting paper is then 0253/400
inches thick. (That is about 2.3 × 1013 inches and about 355 million miles!)
Fifteen Fibonaccis. List the first 15 Fibonacci numbers. - correct answer-1, 1, 2, 3, 5, 8, 13,
21, 34, 55, 89, 144, 233, 377, 610
Born φ. What is the precise number that the symbol φ represents? What sequence of
numbers approaches φ? Choose all correct answers. - correct answer-The symbol φ
represents the infinitely long fractal expression / The symbol φ represents a solution to the
equation / A sequence of numbers that approaches φ is the list of ratios of consecutive
Fibonacci numbers.
This question gave the Fibonacci sequence its name. It was posed and answered by
Leonardo of Pisa, better known as Fibonacci. Suppose we have a pair of baby rabbits: one
male and one female. Let us assume that rabbits cannot reproduce until they are one month
old and that they have a one - month gestation period. Once they start reproducing, they
,produce a pair of bunnies each month (one of each sex). Assuming that no pair ever dies,
how many pairs of rabbits will exist in a particular month? During the first month, the bunnies
grow into rabbits. After two months, they are the proud parents of a pair of bunnies. There
will now be two pairs of rabbits: the original, mature pair and a new pair of bunnies. The next
month, the original pair produces another pair of bunnies, but the new pair of bunnies is
unable to reproduce until the following month. Thus we have:
Continue to fill in this chart and search for a pattern - correct answer-1, 1, 2, 3, 5, 8, 13, 21
Discovering Fibonacci relationships (S)
We'll use the symbol F1 to stand for the first Fibonacci number, F2 for the second Fibonacci
number, F3 for the third Fibonacci number, and so forth. So F1 = 1, and F2 = 1, and,
therefore, F3 = F2 + F1 = 2, and F4 = F3 + F2 = 3, and so on. In other words, we write Fn for
the nth Fibonacci number where n represents any natural number; for example, we denote
the 10th Fibonacci number as F10 and hence
we have F10 = 55. So, the rule for generating the next Fibonacci number by adding up the
previous two can now be stated, in general, symbolically as:
Fn = Fn − 1 + Fn − 2
By experimenting with numerous examples in search of a pattern, determine a simple
formula for (Fn +1)2 + (Fn)2; that is, a formula for the sum of the squares of two consecutive
Fibonacci numbers. - correct answer-(Fn +1)2 + (Fn)2 = F2n + 1 for n ≥ 01
Sum of Fibonacci (H). Express each of the following natural numbers as a sum of distinct,
nonconsecutive Fibonacci numbers: 356, 948, 610, 1289.
In each case, enter the Fibonacci numbers in descending numerical order: 356, 948, 610,
1289 - correct answer-356= 233, 89, 34
948= 610, 233, 89, 13, 3
610= 610
1289= 987, 233, 55, 13, 1
Sum of Fibonacci. Express the natural number 31 as a sum of distinct, nonconsecutive
Fibonacci numbers given in descending order (e.g. 55+21+3). - correct answer-21+8+2
Primal instincts. List the first 15 prime numbers. - correct answer-2, 3, 5, 7, 11, 13, 17, 19,
23, 29, 31, 37, 41, 43, 47
Fear factor. Express each of the following numbers as a product of primes: 77, 7889, 8, 39,
5643. - correct answer-77 = 7 x 11
7889 = 7 x 7 x 7 x 23
8=2x2x2
39 = 3 x 13
5643 = 3 x 3 x 3 x 11 x 19
, Odd couple. If n is an odd number greater than or equal to 3, can n + 01 ever be prime?
What if n equals 01? - correct answer-No. Then n + 01 is prime.
Always, sometimes, never. Does a prime multiplied by a prime ever result in a prime? Does
a nonprime multiplied by a nonprime ever result in a prime? Always? Sometimes? Never?
Explain your answers. - correct answer-Never, by definition.
Never, by definition.
Twin primes. Find the first 15 pairs of twin primes. - correct answer-(3,5), (5,7), (11,13),
(17,19), (29,31), (41,43), (59,61), (71,73), (101,103), (107,109), (137,139), (149,151),
(179,181), (191,193), (197,199)
Floating in factors. What is the smallest natural number that has three distinct prime factors
in its factorization? - correct answer-30
You own a very expensive watch that is currently flashing "7:15." What time will it read in 12
hours? In 17 hours? In 26 hours? In 336 hours? What time is it when an elephant sits on it? -
correct answer-In 12 hours it will read 7:15
In 17 hours it will read 12:15
In 26 hours it will read 9:15
In 336 hours it will read 7:15
Living in the past. Your watch currently reads "2:45." What time did it read in 24 hours
earlier? Three hours earlier? Thirty-one hours earlier? What time did it read 2400 hours
earlier? - correct answer-24 hours earlier it read 2:45
Three hours earlier it read 11:45
Thirty-one hours earlier it read 7:45
2400 hours earlier it read 2:45
Hours and hours. The clock now reads 10:45. What time will the clock read in 60 hours?
What time will the clock read in 860 hours?
Suppose the clock reads 07:30. What did the clock read 28 hours earlier?
What did the clock read 96 hours earlier? - correct answer-10:45
6:45
3:30
7:30
Celestial seasonings (S). Which of the following is the correct UPC for Celestial Seasonings
Ginseng Plus Herb Tea? Show why the other numbers are not valid UPCs. - correct
answer-Check sum for 0 70743 00021 8 = 42
Check sum for 0 70734 00021 8 = 40
Check sum for 0 71734 00021 8 = 43
