ABACUS International Math Challenge
for
3rd and 4th graders
November, 1998
A.81. You write the following four numbers
on the blackboard: 1, 9, 9, 8. In every step you pick two of these numbers,
erase them and replace them with numbers one greater then the ones you erased.
With such steps, can you manage to have four identical numbers on the blackboard?
A.82. When I was 8 years old my father
was 31. Now he is twice as old as I am. How old I am?
A.83. Is the sum of the first 100 prime
numbers even or odd?
A.84. In the following addition the same
letters mean the same digits, different letters mean different digits. What
number is ABCDACE?
A.85. We wrote the numbers 1, 2, 3, ...
, 11 on separate sheets of paper, one number on every sheet. We mixed them
and separated them into two boxes. Andy added the numbers in one of the
boxes, and Bea did the same thing with the other box. Then Bea said:
"Interesting! My number is six times as big as Andy's."
Is this possible?
A.86. Draw eight segments of a straight
line so that every one of them should intersect three others.
A.87. In an office the boss puts a letter
on his secretary's desk in different parts of the day for her to type it
up. He always gives one letter at a time and always puts it on top of the
other letters that were already on the desk. The secretary, when she has
time, takes a letter from the top of the pile and types it up. If there
are 5 letters, and the boss put them down in the 1-2-3-4-5 order, in which
of the following orders is impossible for the secretary to type these letters?
A) 1-2-3-4-5
B) 2-4-3-5-1
C) 3-2-4-1-5
D) 4-5-2-3-1
E) 5-4-3-2-1
A.88. How can you cut up a square into
10 smaller squares?
Please, send your solutions to: