**dan's math@home - problem of the week - archives****Problem Archives**page 14**Problems Only.**For answers & winners click here.**1-10****. 11-20 . 21-30 . 31-40 . 41-50 . 51-60 . 61-70 . 71-80 . 81-90 . 91-100****101-110****. 111-120 . 121-130 . 131-140 . 141-150 . 151+ .**prob index131 - Back at the 7-11 132 - - The Top Five ! 133 -- Walk, Eat, Bike 134- A Peachy Quintet 135 - Reciprocal Pairs 136 How Lo CanUGo 137 -- 2000 Shuffles ! 138 The Twelve Coins 139 - A Funny Inverse 140 Swimr Loses Cap - Problem #131 - Posted Tuesday, October 16, 2001
- Back at the 7-11! (back to top)
- When Jack went back for a late-night snack, he bought three items off the rack. Zack
- rang up the snacks and said "5.70, Jack." "Wait, Zack, you multiplied the prices instead
- of adding!" "Multiply, add; it still comes out the same. Pay up." What the hack is going
- on here at the Snack'n'Shack?! (What were the prices of Jack's three items?)
- Problem #132 - Posted Friday, October 26, 2001
- The Top Five (back to top)
- Five bicyclists tried to predict their order of finish in a race. Alice, Bert, Charlie, Daria, &
- Ernie, the only entrants, spoke . . . Alice: "Bert will finish two places higher than Charlie."
- Bert: "I'm gonna finish in third place, you just watch me." Charlie: "Daria will be first."
- Daria: "Bert'll finish second." Ernie: "Charlie will be three places lower than Alice."
- It turned out only one was correct: the eventual winner. There were no ties.
- What were their places in the race?
- Problem #133 - Posted Saturday, November 3, 2001
- Walk, Eat, Bike (back to top)
- A woman walks to her friend's house at R mph. It takes her T hours, and she spends S
- hours having lunch with her friend. She borrows a bicycle for the trip home, but must
- follow a path that's U times as long as the walking path. If she bikes N times as fast as
- she walks, what is her total elapsed time for the round trip? (Including lunch!)
- Clues for integers R , T , S , U , and N : RTSUN = 72 ; R+T+S+U+N = 13 ; U > N > S ;
- a majority of R , T , S , U , N are prime numbers ; RT = S + UN ; {R,T,S,U,N} has four elements.
- Problem #134 - Posted Monday, November 12, 2001
- A Peachy Quintet (back to top)
- Here are five sweet number puzzles, each is a 'peach'.

- a) If 3^n = 4 and 4^m = 8, then how much is 9^(n - m) ?
- b) What number is three times the sum of its two digits ?
- c) This is the smallest factorial that's a multiple of 2^22 .
- d) A fraction between 34/45 and 43/54 with denom < 100 ?
- e) The number of primes whose squares have 4 or 5 digits ?
- Problem #135 - Posted Thursday, November 22, 2001
- Reciprocal Pairs (back to top)
- Find all solutions (that you can) to : 1/x + 1/y = 1/14 :
- a) where x and y are positive integers, x <= y ,
- b) where x and y are any integers and x <= y .
- Problem #136 - Posted Tuesday, December 4, 2001
- How Low Can You Go ? (back to top)
- If each of the letters A, B, and C represents a different digit, what is the MINIMUM value of
- (ABC) / (A+B+C) ? NOTE: In ABC, A is the hundreds digit, B is the tens digit, and
- C is the ones digit - - they
are
__not__multiplied. - Problem #137 - Posted Saturday, December 15, 2001
- 2000 Shuffles ! (back to top)
- A
__shuffle__of 2n cards puts the first n cards in the odd positions and the last n cards - in the even positions.[For example shuffle (1,2,3,4,5,6) and you get (1,4,2,5,3,6).]
- Heather has 10 cards, 1-10, Briana has 12 cards, 1-12. Each shuffles her deck 2000
- times. "Hey, my deck is back to its original state!" Who said that, and which card
- does the other deck have in position #5?
- Problem #138 - Posted Wednesday, December 26, 2001
- The Twelve Coins (back to top)
- I just got twelve rare coins as a gift, all identical in apperance. I know one is a fake; it's too
- light or too heavy (I'm not sure which). I do have a balance scale with two pans. How can
- I tell which is the fake coin (and whether it's light or heavy) in only three weighings ?
- Problem #139 - Posted Tuesday, January 8, 2002
- A Funny Inverse ! (back to top)
- Many of my algebra and precalculus students think the 'inverse function' of f(x), often
- written f^(-1)(x), is the same as the reciprocal 1/f(x) (mistaking the -1 for an exponent).
- This (as I am obliged to remind them) is almost always false. But can you find at least
- one function whose inverse is also its reciprocal? Tiebreaker: Find as many as you can!
- Problem #140 - Posted Monday, January 28, 2002
- Swimmer Loses Cap ! (back to top)
- As a swimmer jumps off a small bridge and begins to swim upstream,
- her swim cap comes off and floats downstream. Ten minutes later she turns
- around, swimming downstream with the same effort, past her original bridge.
- At the next bridge, 1000 meters away from the first, she catches the cap.
- What was the speed of the current? Of the swimmer?
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