ABACUS International Math Challenge
for
7th and 8th graders
November, 1999
C.145. Could the number 1999p+1 be a prime,
if p is a prime?
C.146. The sum of 10 positive whole numbers
is 1001. What could the highest possible greatest common factor of these
numbers be?
C.147. Using every number, put the numbers
1, 2, 3, 4, 5, 6, 7, and 8, in the circles so that the sum of the numbers
in each of the column and row of 3 circles is:
a) 13
b) 12.
C.148. The sides of a rectangle are 5 and
9 units. We cut up this rectangle into 10 smaller rectangles with whole
number-long sides each. Prove that at least two of them must have the same
area.
C.149. Five men are taking measurements
on a plane: Danny is 2 km from Erwin, Erwin is 1650 m from Frank, Frank
is 8.5 km from George, George is 3.75 km from Henry, and Henry is 1100 m
from Danny. How far is Henry from Erwin?
C.150. There were three times as many men
as women on a party. After 4 men left with their wives, there were four
times as many men as women. How many men and women attended the party?
C.151. You are planting sprouts on a grid
in a rectangular garden bed. How many rows and how many columns do you have
to have if you want to have the same number of sprouts on the perimeter
as the number of sprouts inside of the perimeter?
C.152. The square of a fraction (a/b, where
a>1, b>1 whole numbers) is between 4 and 5. Which one of these fractions
has the smallest denominator?
Please, send your solutions to: