- A farmer's cat ran up a tree,
Which was seventy feet and three;
Every day, he went up eleven,
Every night, he came down seven.
Tell me, if he did not drop,
When his feet would reach the top.
- How many possible batting orders are there for a baseball team of nine players?
- If the measures of the angles of a triangle are in the ratio of 1:2:3, determine the ratio of the longest side to the shortest side.
- The sides and height of a triangle are four consecutive whole numbers.
What is the area of the triangle?
- Divide the number 45 into four parts (that is, 4 numbers whose sum is 45), in such a manner that if you
add 2 to the first,
subtract 2 from the second,
multiply the third by 2,
and divide the fourth by 2,
the result in each case will be equal.
What are the four numbers?
- A multiple of eleven I be,
Not odd, but even you see:
My digits (a pair),
When multiplied there,
Make a cube and a square out of me.
Determine the number.
- Mary is 24 years old. If Mary is twice as old as Ann was, when Mary was as old as Ann is now,
how old is Ann now?
- A woman found $2 and then had 5 times as much money as she would have had if she had lost $2 instead.
How much money did she have originally?
- Mr. P went up a hill at the rate of 1.5 mph and came down the same hill at the rate of 4.5 mph, so that it took him 6 hours to make the round trip.
Can you tell how far it was to the top of the hill?
- In two games between two football teams, the Lobos and the Lambkins, the total number of points scored by both teams was 58.
The Lobos did not score in the first game but won the second game by a margin of 10 points, although the Lambkins scored one and a half
times as many points as they did in the first game.
What were the scores in the two games?
- There are 100 teams entered in a single elimination tournament.
Winners play until only one team is left.
What is the total number of games that must be played?
Do not count byes as games played.
- 6 + 4 = 210
9 + 2 = 711
8 + 5 = 313
5 + 2 = 37
7 + 6 = 113
9 + 8 = 117
10 + 6 = 416
15 + 3 = 1218
?? + ?? = 123
- Alice bought 4 items in a store.
The clerk mulitplied the prices together and came up with $7.11, which was the same answer Alice got by adding the four amounts together.
What were the four amounts?
- A boy on being asked the age of himself and of his sister replied:
"Three years ago I was seven times as old as my sister;
Two years ago I was 4 times as old;
last year I was three times as old;
and this year I am 2 and one-half times as old."
What are their ages?
- A piggy bank contained exactly 100 coins having a value of five dollars.
How many different kinds of coins were there and how many of each were in the piggy bank?
- You are a cyclist in a cross-country race. Just before the crossing finish line, you overtake the person in second place.
In what place did you finish?
- What three positive integers have the same product and sum?
- You have a 3-gallon jug and a 5-gallon jug. You need to measure out exactly 7 gallons of water.
How can you do it?
- A man is looking at a photograph of someone. His friend asks who it is.
The man replies, "Brothers and sisters, I have none. But that man's father is my father's son."
Who was in the photograph?
- A man wanted to encrypt his password but he needed to do it in a way so that he could remember it. He had to use seven characters consisting of letters
and numbers only (no symbols like ! or <).
In order to remember it, he wrote down "You force heaven to be empty."
What is his password?
- The number 8,549,176,320 is a unique number. What is so special about it?
- In the first week of the baseball season, James gets 5 hits out of 11 at bats.
In the first week of the baseball season, Jackson gets 3 hits out of 7 at bats.
Who had the better batting average for the first week?
In the second week of the baseball season, James gets 6 hits out of 9 at bats.
In the second week of the baseball season, Jackson gets 9 hits out of 14 at bats.
Who had the better batting average for the second week?
Who had the better batting average for the total of the first two weeks?
- Libby's mother had 4 children.
The first child was named April, the second was named May, the third June.
What was the 4th child called?
- If it takes 5 elves 5 minutes to make 5 dolls, how long would it take 100 elves to make 100 dolls?
- If you look at a clock and the time is 3:15, how many degrees are in the angle between the hour and the minute hands?
- Here is a poem from Bhaskara's Lilavati which poses a math problem about the number of bees.
Can you determine the number of bees in the swarm?
The square root of half the number of a swarm of bees is gone to a shrub of jasmine;
and so are eight-ninths of the whole swarm:
a female is buzzing to one remaining male that is humming
within a lotus in which he is confined, having allured to it by its
fragrance at night. Answer Oh, lovely woman.. the number of bees.
- The poet Longfellow, in his novel, Kavanaugh, introduced several clever mathematical
problems from an ancient Sanskrit work. One follows...
"If one fifth of a bee hive of bees flew to the ladamba flower,
one third flew to the slandbara, three times the difference of these two numbers flew to an arbor,
and one bee continued to fly about attracted on each side by fragrant ketaki and the malati,
what was the number of bees?"
-
If a ball is hit from the corner of a Carom Billiard Table at a 45° angle, and if the ratio of the sides
is p:q (expressed in reduced form),
Then determine a formula for the number of times the ball rebounds before reaching a corner
(answer should be in terms of p and q).
Note: A carom billiard table has no pockets.
-
Given two real numbers a and b, write one expression equal to the smaller of the two numbers.
In other words, write an expression for the piecewise defined expression:
This problem is found in Michael Steuben's book, Twenty Years Before the Blackboard
-
ABC is an isosceles triangle in which AB = AC.
BE is a line segment intersecting angle B, such that angle DBE = 20° and angle CBE = 60°.
A line segment CD intersects angle C, such that angle ECD = 30°.
ED is Joined.
Determine the measure of angle DEB.
-
At a small school, there are just three teachers: Ms. Shickle, Ms. Muller, and Ms. Pleacher.
Each teacher is knowledgeable in the subjects she teaches.
There are five subjects taught: English, mathematics, history, geography, and French.
You are told the following:
Each teacher teaches three subjects.
Ms. Pleacher does not know what an obtuse angle is.
Ms. Muller is the only teacher who knows where the Gobi desert is located.
Ms. Shickle is no good at foreign languages.
No subject is taught by all three teachers.
Which subjects does each teacher teach?
-
Travis, Trip, and Thomas and their wives Tricia, Tina, and Tracey live in the same town.
A. Travis is a keen golfer but does not sail.
B. Trip lives next door to Tricia and he is a good sailor.
C. Thomas' daughter used to babysit for one of Tina's children.
D. Tricia has two daughters.
E. Tina's husband is the only one of the men who lives within walking distance of the
railroad station.
F. Tracey is not too good at tying knots.
Can you pair the wives off with their husbands?
-
A gentleman had a sitting room with only one window in it -- a square window, three feet high and 3 feet wide.
Now he had weak eyes, and the window gave off too much light. So, he called for the builder, and told him to alter it, so
as to give half the light. Only he has to keep it square -- he has to keep it 3 feet wide -- and he has to keep it 3 feet
high.
How did he do it?
Remember, he wasn't allowed to use curtains, or shutters, or colored glass, or anything of that sort.
-- from Lewis Carroll
-
Two travellers spend 6 hours walking along a level road, then up a hill, and then back home.
Their pace on the level road was 4 mph, up the hill was 3 mph, and down the hill was 6 mph.
Determine the total distance that they walked.
Which was seventy feet and three;
Every day, he went up eleven,
Every night, he came down seven.
Tell me, if he did not drop,
When his feet would reach the top.
What is the area of the triangle?
add 2 to the first,
subtract 2 from the second,
multiply the third by 2,
and divide the fourth by 2,
the result in each case will be equal.
What are the four numbers?
Not odd, but even you see:
My digits (a pair),
When multiplied there,
Make a cube and a square out of me.
Determine the number.
How much money did she have originally?
Can you tell how far it was to the top of the hill?
The Lobos did not score in the first game but won the second game by a margin of 10 points, although the Lambkins scored one and a half times as many points as they did in the first game.
What were the scores in the two games?
Winners play until only one team is left.
What is the total number of games that must be played?
Do not count byes as games played.
9 + 2 = 711
8 + 5 = 313
5 + 2 = 37
7 + 6 = 113
9 + 8 = 117
10 + 6 = 416
15 + 3 = 1218
?? + ?? = 123
The clerk mulitplied the prices together and came up with $7.11, which was the same answer Alice got by adding the four amounts together.
What were the four amounts?
"Three years ago I was seven times as old as my sister;
Two years ago I was 4 times as old;
last year I was three times as old;
and this year I am 2 and one-half times as old."
What are their ages?
How many different kinds of coins were there and how many of each were in the piggy bank?
In what place did you finish?
How can you do it?
The man replies, "Brothers and sisters, I have none. But that man's father is my father's son."
Who was in the photograph?
In order to remember it, he wrote down "You force heaven to be empty."
What is his password?
In the first week of the baseball season, Jackson gets 3 hits out of 7 at bats.
Who had the better batting average for the first week?
In the second week of the baseball season, James gets 6 hits out of 9 at bats.
In the second week of the baseball season, Jackson gets 9 hits out of 14 at bats.
Who had the better batting average for the second week?
Who had the better batting average for the total of the first two weeks?
The first child was named April, the second was named May, the third June.
What was the 4th child called?
Can you determine the number of bees in the swarm?
The square root of half the number of a swarm of bees is gone to a shrub of jasmine;
and so are eight-ninths of the whole swarm:
a female is buzzing to one remaining male that is humming
within a lotus in which he is confined, having allured to it by its
fragrance at night. Answer Oh, lovely woman.. the number of bees.
"If one fifth of a bee hive of bees flew to the ladamba flower,
one third flew to the slandbara, three times the difference of these two numbers flew to an arbor,
and one bee continued to fly about attracted on each side by fragrant ketaki and the malati,
what was the number of bees?"
Then determine a formula for the number of times the ball rebounds before reaching a corner
(answer should be in terms of p and q).
Note: A carom billiard table has no pockets.
In other words, write an expression for the piecewise defined expression:
This problem is found in Michael Steuben's book, Twenty Years Before the Blackboard
BE is a line segment intersecting angle B, such that angle DBE = 20° and angle CBE = 60°.
A line segment CD intersects angle C, such that angle ECD = 30°.
ED is Joined.
Determine the measure of angle DEB.
Each teacher is knowledgeable in the subjects she teaches.
There are five subjects taught: English, mathematics, history, geography, and French.
You are told the following:
Each teacher teaches three subjects.
Ms. Pleacher does not know what an obtuse angle is.
Ms. Muller is the only teacher who knows where the Gobi desert is located.
Ms. Shickle is no good at foreign languages.
No subject is taught by all three teachers.
Which subjects does each teacher teach?
A. Travis is a keen golfer but does not sail.
B. Trip lives next door to Tricia and he is a good sailor.
C. Thomas' daughter used to babysit for one of Tina's children.
D. Tricia has two daughters.
E. Tina's husband is the only one of the men who lives within walking distance of the railroad station.
F. Tracey is not too good at tying knots.
Can you pair the wives off with their husbands?
How did he do it?
Remember, he wasn't allowed to use curtains, or shutters, or colored glass, or anything of that sort.
-- from Lewis Carroll
Their pace on the level road was 4 mph, up the hill was 3 mph, and down the hill was 6 mph.
Determine the total distance that they walked.