dan's math@home - problem of the week - archives
Problem Archives page 14

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 index

131 - 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
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
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
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
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
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
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
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
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
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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Problem Archives Index

Probs & answers . 1-10 . 11-20 . 21-30 . 31-40 . 41-50 . 51-60 . 61-70 . 71-80 . 81-90
Problems only . . . 1-10 . 11-20 . 21-30 . 31-40 . 41-50 . 51-60 . 61-70 . 71-80 . 81-90

Probs & answers . . . 91-100 . 101-110 . 111-120 . 121-130 . 131-140 . 141-150 . 151+
Problems only . . . . . 91-100 . 101-110 . 111-120 . 121-130 . 131-140 . 141-150 . 151+

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