**dan's math@home - problem of the week - archives****Problem Archives**page 16**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 index151 Friends, Wives, $ 152- Nearly Isosceles 153- Sharon & Karen 154 - Swim 2D Boat ! 155 - Can You Digit ? - Problem #151 - Posted Wednesday, August 14, 2002
- Friends, Wives, and Money (back to top)
- Lucky Jim won $1,000,000 (a million dollars), split it up and gave it all to three male friends
- and their wives. The wives (together) received just $4,000 short of $400,000. Jane got
- $10,000 more than Catherine, and Marcy got that same amount more than Jane.
- John Green was given as much as his wife, Henry Brown got half again as much as his wife,
- and Tom Cobalt received twice as much as his. What was the first name of each man's wife,
- and how much money did each of the six receive?
- Problem #152 - Posted Sunday, September 1, 2002
- Nearly Isosceles, Right? (back to top)
- Last problem of the 2001-02 contest ! New season starts with Prob 153!
- The most famous Pythagorean Triangle (a right triangle with all integer sides)
- is the < 3 , 4 , 5 > where 3^2 + 4^2 = 5^2. The 'legs', a=3 and b=4, are
- consecutive integers, making a nearly-isosceles right triangle. What are
- the next four smallest integral right triangles with consecutive legs?

- Problem #153 - Posted Wednesday, September 11, 2002
- Sharon & Karen . . . for each other (back to top)
- First problem of the 2002-03 contest! : : This begins my SIXTH season!!
- Two algebra students decide to save time on their homework by sharin' the work equally.
- But after a while Karen has only done three-fifths of the problems that Sharon has left,
- which in turn is four-sevenths of the amount that Sharon has done. How much faster
- must Karen work than Sharon, if they're carin' to finish simultaneously?
- Problem #154 - Posted Saturday, September 21, 2002
- Swim 2D Boat ! (back to top)
- You (A) see a boat (B) tied up across the river and want to reach it in a straight line.
- The total distance straight across to C & then downstream to the boat is 1/5 mile
- longer than the half mile directly from A to B, and AC > CB. The current is 2 mph
- and in still water you swim at 3 mph. a) At what angle (to the nearest degree, from your
- edge of the river) should you point so you drift and exactly reach the boat?
- b) How long (in min. and sec.) will it take you to swim there? Please explain your reasoning.

current : 2 miles per hour

- Problem #155 - Posted Monday, October 7, 2002
- Can You Digit? (A few puzzles about numbers with special digit properties) (back to top)
- a) Find two three-digit numbers, not containing zero, whose squares end in the same 3 digits
- (as the number, in
the same order). (One-digit example:
__5__^2 = 2__5__; both end in 5.) - b) Find two pairs of consecutive three-digit numbers whose squares have the same digits
- (for each pair). (Two-digit example:
13^2 =
__169__, 14^2 =__196__, same digits.) - c) Find a set of six non-zero 1-digit numbers such that the sum of three of them equals the sum
- of the others, and the sum of the squares (of the same three) is the sum of the squares of the others.
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