🚀 go-pugleaf

1. If the sum of m and n is 3 and the sum of the squares of m and n is 
6, 
find the sum of the cubes of m and n.

2. Give  AB = AC
      AE = AD
      angle of BAD = 30 degrees
   Find: angle of EDC?  
	
	 A
	/|\
       / | \ E
      /  | /\ 
    B/___|/__\C
         D     

3. Sally invited 17 guests to her party. She assigned each guest a 
number from 2 to 18, keeping 1 for herself. When everyone was dancing, 
Sally noticed that the sum of each couple's numbers was a perfect 
square. What was the number of Sally's dancing partner?

4. A man who is always in a hurry walks up an up-going escalator at 
the rate of one step per second. Twenty steps brings him to the top. 
The next day he goes up the same escalator at the rate of two steps 
per second, reaching the top in 32 steps. How many steps are there 
in the escalator?


5. If you start at the top and work your way down through the array, 
each move being to an adjacent letter in the row below, how many 
different paths are there when speeling the word "mathematics"?

				M
			      A   A
			    T   T   T
			  H   H   H   H
                	E   E   E   E   E
	 	      M   M   M   M   M   M
		        A   A   A   A   A  
   			  T   T   T   T  
                            I   I   I
                              C   C
                                S

6. Littel Tommy Jones smudged his candy on the wall of the living 
room one foot from the floor and six feet from each side wall. A 
fly with a broken wing is standing on the  opposite wall one foot 
from the ceiling and six feet from each side wall. If the living room 
is thirty feet long, twelve feet high, and twelve feet wide, what is 
the shortest path along which the fly could walk to get from where it 
is to the candy smudge?


7. Three teen-aged boys, Mick, Mel, and Marv, and two teen-aged girls, 
Meg and Mavis, all tired of their regular Saturday chores, determined 
to effect mutually beneficial trades. So with the consent of their 
families, each arranged to do a differnet one of the other's chores 
on four consecutive Saturdays. From this information and the clues 
below, find the full names of the five, their regular chores, and 
who did which chore on which Saturday.
   a. The one whose job it is to weed his family's garden took over 
      the sheep dog bathing two weeks later than Task did.
   b. On three consecutive Saturdays, Mel (in the order given) weeded 
      a garden, did Meg's chore, and filled in for Tackler.
   c. Tiller chose to save the least painful for last and did his two 
      dog-tending jobs on the first two Saturdays.
   d. On the first Saturday, three of the chores done were as follows: 
      Mavis cleaned a fish tank, Toiler did Tender's chore, 
      and Mick vacuumed a car.
   e. The greyhound was exercised on consecutive Saturdays by, first, 
      the one whose regular chore is car-vacuuming and then by Marv.