Read a Book Day (Sept. 6) Meeting
Also ideal for Read Across America Day (March 2)
or Children’s Book Week (May 12-18)
(Multiple Topics)
Topic
There are a variety of math topics covered in the problems used for this meeting. The problems
are not provided in order of level of difficulty.
Materials Needed
♦ Copies of the Read a Book Day problem set (Problems and answers can be viewed here, but
a more student-friendly version in larger font is available for download from
www.mathcounts.org on the MCP Members Only page of the Club Program section.)
♦ Calculators
Meeting Plan
This meeting idea is great to use at a variety of times throughout the year. We have identified
three particular holidays that are relevant: Read a Book Day (Sept. 6), Read Across America
Day (March 2) and Children’s Book Week (May 12-18).
The problems that follow come from a problem set that originally was printed in the 2005–2006
MATHCOUNTS School Handbook. If you use this for your first meeting, we suggest letting the
students work in groups on this set of problems. The difficulty level from problem to problem
varies.
When students are finished with the 10 problems we have provided, encourage them to write
some of their own that are based on books and characters they are familiar with. Students
then can swap papers with each other, or you can consolidate the problems and make another
handout for the next meeting. Also, ask students to keep an eye out for opportunities to create
similar problems based on the books they read throughout the year. Perhaps speak with the
English teachers in your school to see if they have suggestions for problem scenarios based on
the books students will be reading in class.
1. Tweedledum says, “The sum of your weight and twice mine is 361 pounds.” Tweedledee says, “Contrariwise, the
sum of your weight and twice mine is 362 pounds.” If they are both correct, how many pounds do Tweedledum and
Tweedledee weigh together? [Through the Looking Glass by Lewis Carroll]
2. Caractacus Pott invents a candy for which he is paid one shilling for every thousand candies sold. He expects to
sell 5 million candies every year, and one shilling is equivalent to 14 U.S. cents. How much will Caractacus make in
one year in U.S. dollars? [Chitty Chitty Bang Bang by Ian Fleming]
3. Sherlock Holmes states, “If a rod of six feet threw a shadow of nine feet, a tree of 64 feet would throw one of …”
What length, in feet, should Sherlock say next? [Sherlock Holmes: The Complete Novels & Stories, Volume I by Sir
Arthur Conan Doyle]
4. Four children find a magic token that grants half of any wish. Their mother takes the token with her to a destination
20 miles away, and when she wishes she was home, she magically ends up halfway home. If the mother continues to
make the same wish, how many more wishes will it take for her to be within 100 feet of her house? There are
5280 feet in 1 mile. [Half Magic by Edward Eager]
5. Charlie Bucket receives one bar of chocolate on his birthday. He eats one nibble of the same size each day and
manages to make the bar last for 30 days. What percent of his chocolate bar is left after 18 days? [Charlie and the
Chocolate Factory by Roald Dahl]
2008–2009 MATHCOUNTS Club Resource Guide
Club Resource Guide.pdf 21
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8/18/08 11:24:14 AM
6. Milo sees this sign that describes the distance to Digitopolis in six different ways.
According to this sign, how many inches are in a rod? [The Phantom Tollbooth by
Norton Juster]
DIGITOPOLIS
5 miles
1600 rods
8800 yards
26,400 feet
316,800 inches
633,600 half-inches
7. Five men were to share a treasure of gold with Long John Silver. If the treasure were split in the following ratio
2:5:7:10:20:50, and the least amount any of the six pirates received was 14,000 pounds of gold, what is the total
weight of the gold treasure? [Treasure Island by Robert Louis Stevenson]
8. The Emperor of Lilliput gives Gulliver a daily allowance of food and drink that is equivalent to the amount given
to 1728 Lilliputians. If Gulliver’s allowance of food and drink will fit in a cubical box that measures 24 “blots” along
each edge, what is the edge length, in blots, of the cubical box for one Lilliputian’s daily allowance of food and drink?
[Gulliver’s Travels by Jonathan Swift]
9. A ship travels the 200-mile route from Fort Kearney to Omaha at an average rate of 40 miles per hour. The ship
reaches Omaha at 1 p.m. What time did it leave Fort Kearney? (Assume the ship did not cross any time zones.)
[Around the World in Eighty Days by Jules Verne]
10. Alice changes size several times. The ratio of her original height to her second height is 24 to 5. The ratio of her
second height to her third height is 1 to 12. The ratio of her original height to her fourth height is 16 to 1. The tallest of
these four heights is 10 feet. What is her shortest height, in inches? [Alice in Wonderland by Lewis Carroll]
Answers: 241 pounds; $700; 96 feet; 10 wishes; 40%; 198 inches; 658,000 pounds; 2 blots; 8 a.m.; 3 inches
Please share any additional literature-related questions you and/or your club members
create during this meeting or throughout the year. We would love to share these with
other clubs while crediting you for your creativity. Send your submissions to info@
mathcounts.org with the subject line, “MATHCOUNTS Club Program Ideas.” Thank you in
advance!
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Club Resource Guide.pdf 22
2008–2009 MATHCOUNTS Club Resource Guide
8/18/08 11:24:14 AM
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Read a Book Day Meeting
Problem Set
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1. __________ Tweedledum says, “The sum of your weight and twice mine is 361 pounds.”
Tweedledee says, “Contrariwise, the sum of your weight and twice mine is 362 pounds.” If they
are both correct, how many pounds do Tweedledum and Tweedledee weigh together? [Through
the Looking Glass by Lewis Carroll]
2. __________ Caractacus Pott invents a candy for which he is paid one shilling
for every thousand candies sold. He expects to sell 5 million candies every year,
and one shilling is equivalent to 14 U.S. cents. How much will Caractacus make in
one year in U.S. dollars? [Chitty Chitty Bang Bang by Ian Fleming]
3. __________ Sherlock Holmes states, “If a rod of six feet threw a shadow of nine feet, a tree
of 64 feet would throw one of …” What length, in feet, should Sherlock say next? [Sherlock
Holmes: The Complete Novels & Stories, Volume I by Sir Arthur Conan Doyle]
4. __________ Four children find a magic token that grants half of any wish. Their mother takes
the token with her to a destination 20 miles away, and when she wishes she was home, she
magically ends up halfway home. If the mother continues to make the same wish,
how many more wishes will it take for her to be within 100 feet of her house? There
are 5280 feet in 1 mile. [Half Magic by Edward Eager]
5. __________ Charlie Bucket receives one bar of chocolate on his birthday.
He eats one nibble of the same size each day and manages to make the
bar last for 30 days. What percent of his chocolate bar is left after 18 days?
[Charlie and the Chocolate Factory by Roald Dahl]
6. __________ Milo sees this sign that describes the distance to Digitopolis
in six different ways. According to this sign, how many inches are in a rod?
[The Phantom Tollbooth by Norton Juster]
DIGITOPOLIS
5 miles
1600 rods
8800 yards
26,400 feet
316,800 inches
633,600 half inches
Copyright MATHCOUNTS, Inc. 2008. MATHCOUNTS Club Resource Guide Problem Set
7. __________ Five men were to share a treasure of gold with Long John Silver. If the treasure
were split in the following ratio 2:5:7:10:20:50, and the least amount any of the six pirates
received was 14,000 pounds of gold, what is the total weight of the gold treasure, in pounds?
[Treasure Island by Robert Louis Stevenson]
8. __________ The Emperor of Lilliput gives Gulliver a daily allowance of food and drink that is
equivalent to the amount given to 1728 Lilliputians. If Gulliver’s allowance of food and drink will
fit in a cubical box that measures 24 “blots” along each edge, what is the edge length, in blots,
of the cubical box for one Lilliputian’s daily allowance of food and drink? [Gulliver’s Travels by
Jonathan Swift]
9. __________ A ship travels the 200-mile route from Fort Kearney to Omaha
at an average rate of 40 miles per hour. The ship reaches Omaha at 1 p.m.
What time did it leave Fort Kearney? (Assume the ship did not cross any time
zones.) [Around the World in Eighty Days by Jules Verne]
10. _________ Alice changes size several times. The ratio of her original height to her second
height is 24 to 5. The ratio of her second height to her third height is 1 to 12. The ratio of her
original height to her fourth height is 16 to 1. The tallest of these four heights is 10 feet. What is
her shortest height, in inches? [Alice in Wonderland by Lewis Carroll]
**Answers to these problems are on page 22 of the 2008-2009 Club Resource Guide.**
Copyright MATHCOUNTS, Inc. 2008. MATHCOUNTS Club Resource Guide Problem Set
Read a Book Day Solutions (2008-2009 MCP Club Resource Guide)
Problem 1. We can find the weight of Tweedledum and Tweedledee together without finding
their individual weights. Combining both of their statements, we know that three Tweedledums
and three Tweedledees would weigh 361 + 362 = 723 pounds. Tweedledum and Tweedledee
must weigh 723 ÷ 3 = 241 pounds together.
Problem 2. One shilling for every 1000 candies is equivalent to 5000 shillings for every
5,000,000 candies. If every shilling is worth 14 cents, Caractacus Pott will make 5000 × 14 =
70,000 cents or $700 in one year.
Problem 3. A 9-foot shadow is half again as long as the 6-foot rod that casts the shadow (9/6 =
3/2 = 1.5). The shadow of a 64-foot tree will be 3/2 × 64 = 96 feet, so Sherlock Holmes should
say 96 next.
Problem 4. There are 5280 feet in one mile, so 20 miles is equal to 20 × 5280 = 105,600 feet.
The question is how many times do we need to multiply 105,600 feet by 1/2 to make it less than
100 feet. We would need to know about logarithms to solve an inequality such as
105,600 × (1/2)y < 100. We can certainly keep multiplying by 1/2 (or dividing by 2) until the value
drops below 100, but we might start with the educated guess that y = 10. Many Mathletes will
know 210 = 1024, and 105,600 ÷ 1024 will be about 100. In fact, it is 103.125 so we need to
multiply by 1/2 (or divide by 2) one more time. The mother will need to make her wish a total of
11 times, but she already has made the wish once. She will need to make the wish 10 more
times, and then she will be about 51.6 feet from her house.
Problem 5. After 18 days Charlie Bucket has eaten 18/30 or 6/10 or 60% of his chocolate bar,
so 40% of the chocolate bar is left.
Problem 6. According to the sign, 1600 rods is the same as 316,800 inches, so there must be
316,800 ÷ 1600 = 198 inches in a rod.
Problem 7. If the pirates split the treasure in the ratio 2:5:7:10:20:50, then there are a total of
+ 5 + 7 + 10 + 20 + 50 = 94 equal portions of treasure. If the least amount any of the six pirates
received is 14,000 pounds, then that must belong to the pirate who received two equal portions.
This means that one portion must be 14,000 ÷ 2 = 7000 pounds. The total weight of the treasure
must be 94 × 7000 = 658,000 pounds.
Problem 8. Gulliver’s food and drink will fit in a cubical box that measures 24 “blots” along each
edge. This cube has a volume of 24 × 24 × 24 = 13,824 cubic blots. (A student who recognizes
that 1728 is a perfect cube equal to 12 × 12 × 12 will already know that the Lilliputian’s cubical
box measures 2 × 2 × 2 blots.) Dividing 13,824 cubic blots by the 1728 Lilliputians who would
eat an equivalent amount of food and drink, we find that a Lilliputian must eat and drink about
13,824 ÷ 1728 = 8 cubic blots per day. The cube root of 8 is 2, so the cubical box for one
Lilliputian’s daily allowance of food and drink must measure 2 blots along an edge.
Problem 9. It would take 200 ÷ 40 = 5 hours to go 200 miles at 40 miles per hour. If the ship
reaches Omaha at 1 p.m., then it must have left Fort Kearney at 8 a.m.
Problem 10. If the ratio of Alice’s original height to her second height is 24 to 5, then her
second height was 5/24 of her original height. If the ratio of her second height to her third height
is 1 to 12, then her third height was 12/1 × 5/24 = 5/2 or 2.5 times her original height. This was
Copyright MATHCOUNTS, Inc. 2008. MATHCOUNTS Club Resource Guide Solution Set
her tallest stage. If 2.5 times her original height is 10 feet tall, then her original height must have
been 10/2.5 = 4 feet. The ratio of her original height to her fourth height is 16 to 1, which means
her fourth height is 1/16 of 4 feet, which is 1/16 of 48 inches or 1/16 × 48 = 3 inches tall. This is
her shortest height.
Copyright MATHCOUNTS, Inc. 2008. MATHCOUNTS Club Resource Guide Solution Set