dan's math@home - problem of the week - archives
Problem Archives page 16

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

151 Friends, Wives, \$
152- Nearly Isosceles
153- Sharon & Karen
154 - Swim 2D Boat !
155 - Can You Digit ?

Problem #151 - Posted Wednesday, August 14, 2002
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
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
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 = 25; 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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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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