ABACUS International Math Challenge
for
5th and 6th graders
April, 2002
The final deadline for you to send in your solutions to
these problems and all of those posted since September, 2001 is
May 31, 2002.
B.313. How many 3-digit positive whole
numbers contain the digit zero?
B.314. Are there more 3-digit numbers with
only even digits or with only odd digits?
B.315. A watch can show the time, the date,
or the seconds. There is a button on the watch. If you click it, if it is
on time, it will go to date; if it's on date, it will go to seconds; and
if it's on seconds, it will go to time. Also, if it shows the date, it'll
go back to showing time in five seconds. You are in a dark room. You do
not know what it's showing, but you want it to show time. How can you get
it to show time, and how long will it take? (Suppose it takes no time to
press a button.)
by László Miklós Lovász, Sammamish,
Washington, USA
B.316. You have two cups of the same size.
One of them is half way with water and the other cup is half way with wine.
You take a spoonful of the wine from one cup and pour it into the cup with
water in it. After mixing it very well, you take a spoonful of this solution
and pour it into the cup with wine in it. Now there is some water and some
wine in both cups. Which is more: the wine in the cup that had only water
in it, or the water in the cup that had only wine in it originally?
B.317. Cut up a square-shaped cake with
3 cuts so that you could divide it evenly among either three or four children.
B.318. Find all those 5-digit positive
whole numbers that are square and cube numbers, also.
B.319. Find an at least 2-digit number
such that the sum of the digits of its square is also a square number.
B.320. Take a look at the following sequence:
128, 69, 117, 51, 26, 40, 16, 37, ... (Every element here is the sum of
the squares of the digits of the previous element of the sequence. For example:
1^2 + 6^2 = 37) What number is the 100th element of this sequence?
Please, send your solutions to: