ABACUS International Math Challenge
for
3rd and 4th graders
December, 1999
A.153. My uncle said that he saves every
candle-leftover, and he can make a new candle from the wax leftovers of
seven candles. How many candles can he burn if he bought 92 candles?
A.154. There are 12 stops on a bus route.
On one round of the bus there were no two people who got on and off at the
same stops, so any two people took a different trip. How many people could
take this bus on this round the most?
A.155. We put the positive whole numbers
in the following groups: {1}, {2, 3}, {4, 5, 6}, {7, 8, 9, 10}, ...
What is the first number of the 100th group?
A.156. In the following addition different
letters mean different digits, the same letters mean the same digits. What
number is MAREK?
A.157. The following addition is incorrect,
but could be fixed by replacing a particular digit "d" (everywhere
it appears) with a digit "e". Find this digit "d" and
digit "e".
A.158. How many such 5-digit numbers are
there that when read backwards, you get the same number? (For example: one
of these numbers is 12321)
A.159. How many such 2-digit positive whole
numbers are there in which the sum of the digits is odd, and the sum of
the digits of the next consecutive number is odd, too?
A.160. I wrote all of the 3-digit positive
whole numbers on a separate card each, and I put the cards in a hat. At
least how many cards do I have to take out of the hat so that I could be
sure that I took two numbers in which the sum of the digits are the same?
Please, send your solutions to: