ABACUS International Math Challenge
for
5th and 6th graders
November, 1999
B.145. A positive whole number is "beautiful"
if it is equal to the product of its true divisors (divisors that are different
from 1 and the number itself). What is the 10th smallest beautiful number?
B.146. How many 3-digit numbers are there
in which the sum of the digits is the same as the number created by the
first two digits of this 3-digit number?
B.147. Out of two candles with different
length and thickness, the 10 cm long one burns away in 5 hours, and the
other one in 6 hours. If you start burning them at the same time, in 2 hours
they have the same length. How long was the other candle originally?
B.148. Yummy wants to have pancakes for
breakfast, so she tells the chef that she is going to wake up and start
eating at 8 am, and that she would like to have 20 pancakes. It takes the
chef 1 minute to make a pancake, and it takes Yummy 30 seconds to eat a
pancake. How many minutes before Yummy should the chef wake up?
B.149. In the following multiplication:
AB x AB=BCAC
A, B, and C are different digits, and A+B=C.
What could the value of the product be?
B.150. How many 3-digit number-pairs are
there where the difference between the two numbers is 100, and one of them
is divisible by 6, and the other one is divisible by 7?
B.151. 30xy2 in base 5 are numbers where
x and y are not necessarily different. What is the sum of all of these kind
of odd numbers in base 10?
B.152. Is it possible to have 6 points
in the same plane, so that every one of them is one unit distance apart
from exactly three of the other points?
Please, send your solutions to: