ABACUS International Math Challenge
for
5th and 6th graders
March, 2000
B.177. Once I found all those 2-digit prime
numbers that are the sums of 2, 3, 4, or even 5 different prime numbers,
I multiplied them and then I added the digits of this product. How many
divisors does this number have?
B.178. Captain Eyebrow and his brave soldiers
saved the people of Funnyrunny Island from the green dragon. As a present,
the captain received a basket of coconuts from the locals, which he distributed
among his soldiers fairly, but not equally. Mickey monkey received a third
of what Ho-Ho got, Hey-Hey received 25 less than the two others together.
How many coconuts did each soldier receive if there were 95 coconuts in
the basket?
B.179. What is the following sum:
1/(1x2)+1/(2x3)+1/(3x4)+...+1/(1999x2000)
B.180. I gave a value to every vertex of
a cube. The value of an edge is the sum if the values of the vertices at
its ends. The value of a side is the sum of the values of the edges surrounding
it. The value of a cube is the sum of the values of its sides. What is the
value of the cube if the sum of the values of its vertices is 128?
B.181. Place 7 points and 6 straight lines
on a plane so that every one of the lines contains 3 of the 7 points.
B.182. How many triangles are there on
the following picture?
B.183. How many such 8-digit number-series
are there containing only the digits zero and 1, with no two 1's next to
each other?
B.184. Can you cut up an equilateral triangle
into 2000 equilateral triangles?
Please, send your solutions to: