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 . 151-160 . 161-170 . 171-180
181-190 . 191-200 . 201-210 . 211-220 . 221-230 . 231+ . prob index
 
151 Friends, Wives, $
152- Nearly Isosceles
153- Sharon & Karen
154 - Swim 2D Boat !
155 - Can You Digit ?
156 - This Old House
157 - Chop,Skip,Chop
158- Digits in the Bag
159 Money in theHole
160 - Cubes Come 4th
 
 
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? 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 = 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.
 
 
Problem #156 - Posted Saturday, October 19, 2002
This Old House! (back to top)
"Wow, cool house!" my friend said one day. "How old is it?" "Well, my dad was born in it,
and the house was fifteen years old then. And the funny thing is, if you square the house's age,
the first half is my dad's age and the second half is my age!" How old is the house, how old is
my dad, and how old am I? (Try to Solve, not just Search!)
 
 
Problem #157 - Posted Wednesday, October 30, 2002
Chop, Skip, Chop ! (back to top)
"Only the smartest one shall survive," said the executioner. "All of you prisoners will be seated
around this round table. I will chop off the head of the prisoner in seat #1, skip seat #2, chop #3,
etc. Beheaded bodies (and chairs) will be cleared away post haste. When I get to the end I will
continue to chop, skip, chop, until there is but one prisoner remaining, who will then be freed."
a) If there are 13 prisoners, which is the lucky seat number?
b) In the morning, you will be told how many prisoners, n. You must figure out the best seat
quickly, just knowing n. Which seat, k, should you 'head' for, in order to be freed?
 
 
Problem #158 - Posted Saturday, November 9, 2002
Digits In The Bag ! (back to top)
A math wizard has a bag containing the digits 0 through 9, and has used six of them to stick
two different three-digit perfect squares on the foreheads of Ann and Ben; A and B.
Both Ann and Ben know this fact, but each person can see the other person's number only.
The wizard asks Ann: "How many of the digits remaining in my bag can you exactly tell me?"
Ann replies:"Three." If the wizard now asks the same question to Ben, what should he reply?
 
 
Problem #159 - Posted Monday, November 25, 2002
Money In The Hole? (back to top)
Fearless Frank decided to play a fair coin-flip game with probability 1/2 of winning each
bet, and risked 1/m of his fortune (originally A dollars, m>1) at every flip. After 2n games,
Frank has won n games and lost n. Choose and explain the correct answer from this list:
a) Frank has broken even; he still has his A dollars
b) Frank is predictably ahead by a certain amount
c) Frank is predictably behind by a certain amount
(in case b or c give the exact formula in terms of m and n)
d) Frank is now ahead, behind, or even, depending
on the order in which the wins and losses occurred
e) He is ahead, behind, or even, depending on m and n
 
 
Problem #160 - Posted Saturday, December 7, 2002
Cubes Come Fourth ! (back to top)
A long time ago, I noticed that 65 was the smallest integer that could be written as
the sum of two (different) squares in two different ways: 65 = 8^2 + 1^2 = 7^2 + 4^2.
a) A very famous number is the smallest integer that can be written as the sum of
two cubes in two different ways. What is this number, and why is it famous?
b) What is the smallest integer that's the sum of two different fourth powers in two
different ways? Be sure to say what all those cubes & fourth powers are.
 
 
 
THANKS to all of you who have entered, or even just clicked and looked.
My website is now in its sixth season - over 32,000 hits so far! (Not factorial.)
Help it grow by telling your friends, teachers, and family about it.
YOU CAN ALWAYS FIND ME AT dansmath.com - Dan the Man Bach - 2003 A.D.
 
 
Problem Archives Index
 
Probs & answers . 1-10 . 11-20 . 21-30 . 31-40 . 41-50 . 51-60 . 61-70 . 71-80 . 81-90 . 91-100
Problems only . . . 1-10 . 11-20 . 21-30 . 31-40 . 41-50 . 51-60 . 61-70 . 71-80 . 81-90 . 91-100
Probs & answers . 101-110 . 111-120 . 121-130 . 131-140 . 141-150 . 151-160 . 161-170 . 171-180
Problems only . . . 101-110 . 111-120 . 121-130 . 131-140 . 141-150 . 151-160 . 161-170 . 171-180
Probs & answers . 181-190 . 191-200 . 201-210 . 211-220 . 221-230 . 231+
Problems only . . . . 181-190 . 191-200 . 201-210 . 211-220 . 221-230 . 231+
 
Browse the complete problem list, check out the weekly leader board,
or go back and work on this week's problem!
 
(back to top)
 
[ home | info | meet dan | ask dan | matica | lessons | dvc ]
 
This site maintained by B & L Web Design, a division of B & L Math Enterprises