ABACUS International Math Challenge
for
5th and 6th graders
April, 2000
B.185. Which number is greater:
or 
?
B.186. There are the same number of black
sox and white sox of the same size in a bag. You know that the least number
of sox you have to take out of the bag blind-folded in order to have a pair
of sox of the same color is the same as the least number of sox you have
to take out in order to have two different sox. How many sox are there in
the bag if there is no difference between a left sock and a right sock?
B.187. There are two cell-cultures with
an initial zero number of cells. You add 80 cells to the first culture at
every 10th second and then you put half of the cells from the first culture
to the second culture. In the second culture half of the cells die every
20 seconds starting in the 19th second of this experiment. What is happening
in the 50th second?
B.188. The minute hand of a clock is exactly
above the hour hand for example at 12 noon. When will they be in the same
straight line again next time?
B.189. Can you cut up a horseshoe into
6 pieces with two straight cuts? You may not move around the pieces you
got after the first cut.
B.190. Three fussy children, A, B, and
C, will be taken to a bus trip. Their teacher wants to have them sit in
the same row on seats number 1, 2, and 3. However, they have the following
requests:
- If A sits on seat 1 then B wants to sit on seat 2.
- If B is not sitting on seat 1 then C would like to sit on seat 2.
- If C sits on seat 3 then A would like to sit on seat 1.
Can you sit these children fulfilling all of their requests?
B.191. The heights of the starting 5 players
of the New York Knicks basketball team this year are all different. How
many different ways can they march onto the court in a line, so that none
of them is in between two taller players?
B.192. You may use 5 colors to color all
the vertices of an equilateral triangle. How many different ways can you
do this? Two colorings are different if the final results cannot be matched
by rotations and/or reflections?
Please, send your solutions to: