-
- Problem #201 - Posted Sunday, May 9, 2004
- Couples Buy Books (back to top)
- Two men, David and Clifton, and their wives, Kim and Allison, go out shopping
- for books. Each person paid for each book a number of dollars equal to their
- number of books. David bought 1 more book than Kim, while Allison bought
- only 1 book. If each couple spent the same two-digit sum, who is Kim's husband?
- Show reasoning carefully.
- Problem #201 - Posted Sunday, May 9, 2004
-
- Problem #202 - Posted Thursday, May 20, 2004
- Magic Square Primes (back to top)
- Choosing nine distinct integers from 1-25, make a magic
- square with as many primes as possible. (The example has 4
- primes but you can do better. Note there are 9 primes from 1-25: 2,3,... ,23)
- The winner will be determined using the following comparisons:
- 1) The most primes, 2) Smallest magic constant , 3) order received.
- A magic square has rows, columns, and main diagonals that add
- up to the same thing, the "magic constant." Show reasoning carefully.
- Problem #202 - Posted Thursday, May 20, 2004
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-
- Problem #203 - Posted Wednesday, June 2, 2004
- Where's The Crowd? (back to top)
- My friend's music fan website started out fast: lots of visitors the first week.
- But every week, there were fewer and fewer; the second week there was one
- more visitor than 2/3 of the first week, the 3rd week there were 2 more than
- 2/3 of the second week, the 4th week there were 3 more than 2/3 of the 3rd
- week, and so on, until the final week, when there were just 533. How many
- weeks was the website up, how many visitors did it get the 1st week, and how
- many total visitors were there? Show reasoning carefully.
- Problem #203 - Posted Wednesday, June 2, 2004
- Being a perfect square is
a relative thing. If these
are, find their square
roots in their
- domains (m, n are integers); if not, prove they can't be squares of the given form.
- Is a = 205879238043281 the square of a regular integer? What about b = 205889238043281 ?
- Is c = 1357 + 874 i the square of a Gaussian integer m + n i ? What about d = 573833 + 595944 i ?
- Is e = 275643 + 187110 \/ 2 the square of any m + n \/ 2 ? What about f = 41289 + 43589 \/ 2 ?
- Is g = 71257 + 40976 \/ 3 the square of any m + n \/3 ? What about h = 1967856 - 1136159 \/ 3 ?
- Show reasoning carefully.
- domains (m, n are integers); if not, prove they can't be squares of the given form.
-
- Problem #205 - Posted Monday, June 28, 2004
- Orange Pyramids (back to top)
- The grocery person likes to stack the oranges
- in tetrahedral piles; triangular-based pyramids.
- Each orange is exactly 10 centimeters in diameter.
- a) Exactly how tall (in cm) is a pile of 10 oranges ?
- b) How many oranges are in a pyramid of n layers ?
- c) Exactly how tall is that pile of n layers of oranges ?
- Show reasoning carefully.
- Orange Pyramids (back to top)
- Problem #206 - Posted Tuesday, July 13, 2004
- Given the GCD and LCM (back to top)
- A while ago, I gave my Prealgebra class a puzzle problem: Given two natural numbers,
- m and n. If their GCD is G=6 and their LCM is L=96, what are the numbers ?
- I was surprised when more than one correct answer came in! a) What were all possible
- (m, n) for G=6 and L=72 (m<=n) ? b) What's the smallest sum, m+n, for any (m, n) pair
- that share the same G=gcd and L=lcm (with another m<=n; G>=2)? c) Find the (G, L) pair
- with the most solutions (m, n) for the same G=gcd(m,n) and L=lcm(m,n) (G>1, L < 1001).
- GCD = greatest common divisor ; LCM = least common multiple. Show reasoning carefully.
- Given the GCD and LCM (back to top)
- Problem #207 - Posted Thursday, July 22, 2004
- Lost Bill of Sale (back to top)
- There were six prices for various TV sets sold at the store: $231, $273, $429, $600.60,
- $1001, and $1501.50. One day, a motel owner came in and bought a bunch of TVs.
- The total came to $13519.90 but the bill of sale was lost. How many of each TV
- type did the motel guy buy? Show reasoning carefully.
- Lost Bill of Sale (back to top)
- Problem #208 - Posted Monday, August 2, 2004
- The Third Degrees (back to top)
- Can you find a triangle, whose sides are all equal to
- their opposite angles, in degrees? Prove your answer
- is unique or prove it's impossible. Show reasoning clearly.
- The Third Degrees (back to top)
- Problem #209 - Posted Wednesday, August 11, 2004
- When Cosines Collide (back to top)
- Figure out these three trig treats, give the exact answers with proof.
- a) cos 15 * cos 75 = ? . . . b) cos 20 * cos 40 * cos 80 = ??
- c) cos 18 cos 42 - cos 48 cos 72 = ???
- Show reasoning clearly; all angles are in degrees.
- When Cosines Collide (back to top)
- Problem #210 - Posted Saturday, August 21, 2004
- You contestants come from many countries, but we all speak
the odd language of math!
- a) Prove that if a, b, and c are odd integers, then a x^2 + b x + c = 0 has no
- rational roots. b) (Optional) State what country you're from; I'll put your national flag
- next to your entry; top 3 scores get medals! Show reasoning clearly.
- a) Prove that if a, b, and c are odd integers, then a x^2 + b x + c = 0 has no
