ABACUS International Math Competition
for
5th and 6th graders
January, 1998
B.33. Could 19981998 be the product of three
consecutive whole numbers?
B.34. Could 19981998 be the sum of three
consecutive whole numbers?
B.35. 1998 tennis players participate in
a single elimination championship. In every round players winning the game
advance to the next round, the losers go home. A player with no opponent
in a round automatically advances to the next round. How many games is needed
to find the best player?
B.36. How many 3-digit numbers are there
in which the digits are in an either increasing or decreasing order? (For
example: in 114 the digits are in an increasing order!)
B.37. How many 4-digit-numbers are there
in which there is at least one 1 or 2 among the digits?
B.38. What is the sum of all those 3-digit
numbers with no other digits than 4, 5, 6 or 7?
B.39. Let's suppose that you may go up
on a staircase by taking one or two stairs at a time. (After every step
you may decide whether you want to take one or two stairs on your next step.)
How many different ways can you get up to the 10th stair?
B.40. Using every digit only once, write
down 3 whole numbers with a ratio of 2:3:4.
Please, send your solutions to:
Solutions of previous
problems