- dan's math@home - problem
of the week - archives
- Problem Archives
- Problems Only.
For answers & winners click here.
- 101-110 . 111-120 . 121-130
. 131-140 . 141-150 . 151+
- 11 -Impossible Twins?
- 12 -The ABC's of Cars
- 13 - Spider and the Fly
- 14:Intersecting Bubbles
- 15 -The Right Numbers
- 16 -The Magic Number
- 17 - How Many Ants ?
- 18-What Time Was It?
- 19 - World Cup Soccer
- 20:The Average Speed?
- Problem #11 - Posted Thursday, March 12, 1998
- Impossible Twins? (back
- Anna, the older twin, was
born three hours before her younger sister Lana. On Lana's 21st
birthday, they both went out to a club with some friends. The
bouncer was checking ID's and let Lana go in. But when the older
Anna tried to follow her in, the bouncer said, "I'm sorry,
your 21st birthday isn't for another two days." How
is this possible? Explain fully and correctly to win the contest.
- Problem #12 - Posted Wednesday, March 25, 1998
- The ABC's of Cars (back
- The student parking lot has
81 cars in it; all Acuras, Beetles, and Camrys. There are half
as many Acuras as Beetles, and the number of Camrys is 80% of
the number of Acuras and Beetles together. How many of each kind
of car is in the parking lot?
Show all steps to win contest!
- Problem #13 - Posted Monday, April 6, 1998
- The Spider and the Fly (back to top)
- A spider, in the top-left-front
corner of a 10 x 10 x 10 foot room, sees a big fat fly in the
bottom-right-back corner. Describe the shortest path, and the
length of the path, that the spider can crawl to get the fly.
That's crawl, not jump, fly or spider-web
express! Your explanation must be clear. (Not affiliated with
the squished fly from Problem #2.) ;-}
- Problem #14 - Posted Wednesday, April 15, 1998
- The Intersecting Bubbles (back
- Two overlapping spherical
soap bubbles, whose centers are 50 mm apart, have radii 40 mm
and 30 mm. What is the diameter D of their circle of intersection?
- Problem #15 - Posted Friday, April 24, 1998
- The Right Numbers (back
- (a) The area and volume of
a certain sphere are both 4-digit integers times Pi. What is
- (b) The integers 1, 3, 8,
and N have the property that the product of any two, when added
to 1, gives a perfect square. What is the smallest positive integer
value of N?
- Problem #16 - Posted Tuesday, May 5, 1998
- The Magic Number (back
- A certain six-digit number
is split into two parts; the first three digits and the last
three digits are added (as 3-digit
numbers), the resulting
sum is squared, and the answer is the original 6-digit number!
What was the number? (There might
be more than one answer!)
- Problem #17 - Posted Friday, May 15, 1998
- How Many Ants? (back
- At least a dozen ants are
marching through my kitchen! If the ants walk in rows of
- 7, 11, or 13, there are 2
ants left over, while in rows of 10, there are 6 left over.
- What is the smallest number
of ants there could be?
- NOTE / HINT: A fun trick is to get
someone to use a secret 3-digit number; have them multiply it
- then the answer by 11, then that answer
by 13. They tell you the result, and you "guess" the
- Problem #18 - Posted Monday, May 25, 1998
- What Time Was It? (back to top)
- A basketball playoff game
started between 3pm and 4pm, and ended between 6pm and 7pm.
- The positions of the minute
hand and the hour hand were reversed at the end of the game,
- compared to the beginning.
What was the exact time the game started and ended,
- and how long was the game? (Try
to give exact times, not rounded to the nearest anything.)
- Problem #19 - Posted Tuesday, July 7, 1998 (back from vacation!)
- World Cup Soccer Standings (back
- In this year's Coupe du Monde
98, there are 4 teams in each Group, and they each play each
of the other 3 teams once. Here are the final "Pts standings"
of Groupe C, with the W . L . T
. PTS records (a win is 3 pts and a tie is 1 pt):
- France. . . . . . . 3 . . 0
. . 0 . . 9
- Denmark . . . . 1 . . 1 . .
1 . . 4
- South Africa . .0 . . 1 . .
2 . . 2
- Saudi Arabia. . 0 . . 2 . .
1 . . 1
- How many "Pts standings"
are possible, and are any gettable in more than one way? (not counting order or particular teams) This one would be called 9-4-2-1.
- Problem #20 - Posted Sunday, July 26, 1998 (back to top)
- What's The Average Speed?
- a) Aaron rides his bicycle
at 20 kph (kilometers per hour) to his job, and 30 kph back home
along the same road. What was his average speed for the round
- b) Andy walks 3 mph to his
class. How fast does he have to run back home in order to average
6 mph for the round trip? . . .
Please show your steps and reasoning.
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