UNIV 104 MATH ACTUAL TEST PAPER
WITH VERIFIED ANSWERS
●● Damsel in Distress
Answer: the notorious knight after capturing the damsel took the bridge
away the moat is 20 ft across and has no draw bridge the good knight
stumbled upon two sturdy beams of walking across but they were only
19 ft by 8 inches wide
answer: Use one beam to span the corner and the second beam to cross
onto the ground.
●● The fountain of knowledge
Answer: While on safari, Trey Sheik suddenly found himself alone in
the Sahara Desert. Both hours and miles passed as he wandered
aimlessly through the desert, but he stumbled upon an oasis as he was
nearing dehydration. There, sitting in a shaded kiosk beside a small pool
of mango nectar, was an old man named Al Dente. Big Al not only ran
the mango bar but was also a travel agent and could book Trey on a two-
humped camel back to Kentucky. At the moment, however, Trey desired
nothing but a large drink of that beautifully translucent and refreshing
mangoade. Al informed Trey that he sold the juice only in 8-ounce
servings and the cost for one serving was $3.50. Trey frantically
searched his pockets and discovered that he had exactly $3.50 (along
with a lot of sand). Trey's excitement was soon shattered when Al
casually announced that he did not have an 8-ounce glass - all he had
was a 6-ounce glass and a 10-ounce glass, both with no markings on
,them. And, Al was quite adamant and would only sell Trey exactly 8-
ounces of juice.
answer:Fill the 10-ounce glass and pour juice from this glass into the 6-
ounce glass until it is full - this leaves 4 ounces of juice in the 10-ounce
glass.
Next, empty the 6-ounce glass and transfer the 4 ounces of juice in the
10-ounce glass into the 6-ounce glass
Fill the 10-ounce glass with mango juice and pour juice into the 6-ounce
glass until it is full. Since it already had 4 ounces of juice in it, you can
only add 2 ounces. This leaves you with 8 ounces of juice in the 10-
ounce glass.
●● dropping trou
Answer: The highlight of Professor Burger's April 1993 talk to more
than 300 Williams College students and their parents occurred when,
after remov- ing his shoes, he tied his feet together with a stout rope,
leaped onto the table, dramatically removed his belt, unzipped his
zipper, and dropped his pants. The purple cows (Williams mascots)
mooing about on his baggy boxer shorts completed an image not soon
forgotten in the annals of mathematical talks. The more conservative
parents in the audience were contemplating transferring their sons and
daughters to a less "progres- sive" school.
, But then, at the moment of maximum shock and bewilderment, Profes-
sor Burger performed the seemingly impossible feat of rehabilitating his
fast-sinking reputation. Without removing the rope attached to his feet,
he turned his pants inside out and pulled his trousers back to their accus-
tomed position (though now inside out). Thus he simultaneously
restored his modesty and his credibility by demonstrating the
mathematical tri- umph of reversing his pants without removing the rope
that was tying his feet together.
Please attempt to duplicate Professor Burger's amazing feat—in the
privacy of your room, of course. You will need a rope or cord about 5
feet long. One end of the rope should be tied snugly around one ankle
and the other end tied equally snugly about the other ankle. Now,
without removing the rope, try to take your pants off, turn them inside
out, and put them back on so that you, the rope, and your pants are all
exactly as they were at the start, with the exception of your pants being
inside out.
●● Dodgeball
Answer: Dodgeball is a game for two players—Player One and Player
Two (although any two people can play it, even if they are not named
"Player One" and "Player Two"). Each player has a special game board
(shown below) and is given six turns.
Player One begins by filling in the first horizontal row of his game board
with a run of X's and O's. That is, on the first line of his board, he will
write either an X or an O in each box. Then Player Two places either an
X or an O in the first box of her board. So at this point, Player One has
filled in the first row of his board with six letters, and Player Two has
filled in the first box of her board with one letter.
WITH VERIFIED ANSWERS
●● Damsel in Distress
Answer: the notorious knight after capturing the damsel took the bridge
away the moat is 20 ft across and has no draw bridge the good knight
stumbled upon two sturdy beams of walking across but they were only
19 ft by 8 inches wide
answer: Use one beam to span the corner and the second beam to cross
onto the ground.
●● The fountain of knowledge
Answer: While on safari, Trey Sheik suddenly found himself alone in
the Sahara Desert. Both hours and miles passed as he wandered
aimlessly through the desert, but he stumbled upon an oasis as he was
nearing dehydration. There, sitting in a shaded kiosk beside a small pool
of mango nectar, was an old man named Al Dente. Big Al not only ran
the mango bar but was also a travel agent and could book Trey on a two-
humped camel back to Kentucky. At the moment, however, Trey desired
nothing but a large drink of that beautifully translucent and refreshing
mangoade. Al informed Trey that he sold the juice only in 8-ounce
servings and the cost for one serving was $3.50. Trey frantically
searched his pockets and discovered that he had exactly $3.50 (along
with a lot of sand). Trey's excitement was soon shattered when Al
casually announced that he did not have an 8-ounce glass - all he had
was a 6-ounce glass and a 10-ounce glass, both with no markings on
,them. And, Al was quite adamant and would only sell Trey exactly 8-
ounces of juice.
answer:Fill the 10-ounce glass and pour juice from this glass into the 6-
ounce glass until it is full - this leaves 4 ounces of juice in the 10-ounce
glass.
Next, empty the 6-ounce glass and transfer the 4 ounces of juice in the
10-ounce glass into the 6-ounce glass
Fill the 10-ounce glass with mango juice and pour juice into the 6-ounce
glass until it is full. Since it already had 4 ounces of juice in it, you can
only add 2 ounces. This leaves you with 8 ounces of juice in the 10-
ounce glass.
●● dropping trou
Answer: The highlight of Professor Burger's April 1993 talk to more
than 300 Williams College students and their parents occurred when,
after remov- ing his shoes, he tied his feet together with a stout rope,
leaped onto the table, dramatically removed his belt, unzipped his
zipper, and dropped his pants. The purple cows (Williams mascots)
mooing about on his baggy boxer shorts completed an image not soon
forgotten in the annals of mathematical talks. The more conservative
parents in the audience were contemplating transferring their sons and
daughters to a less "progres- sive" school.
, But then, at the moment of maximum shock and bewilderment, Profes-
sor Burger performed the seemingly impossible feat of rehabilitating his
fast-sinking reputation. Without removing the rope attached to his feet,
he turned his pants inside out and pulled his trousers back to their accus-
tomed position (though now inside out). Thus he simultaneously
restored his modesty and his credibility by demonstrating the
mathematical tri- umph of reversing his pants without removing the rope
that was tying his feet together.
Please attempt to duplicate Professor Burger's amazing feat—in the
privacy of your room, of course. You will need a rope or cord about 5
feet long. One end of the rope should be tied snugly around one ankle
and the other end tied equally snugly about the other ankle. Now,
without removing the rope, try to take your pants off, turn them inside
out, and put them back on so that you, the rope, and your pants are all
exactly as they were at the start, with the exception of your pants being
inside out.
●● Dodgeball
Answer: Dodgeball is a game for two players—Player One and Player
Two (although any two people can play it, even if they are not named
"Player One" and "Player Two"). Each player has a special game board
(shown below) and is given six turns.
Player One begins by filling in the first horizontal row of his game board
with a run of X's and O's. That is, on the first line of his board, he will
write either an X or an O in each box. Then Player Two places either an
X or an O in the first box of her board. So at this point, Player One has
filled in the first row of his board with six letters, and Player Two has
filled in the first box of her board with one letter.
