“Brain Workout” Math Olympiad
1. Jessica borrowed a book from a friend for 3 days. She
read 1/2 of the book on the first day, 1/3 of the rest of the
book on the second day. The number of the pages that
she read during the third day was one half of the number
of pages she read during the first two days. Was Jessica
able to finish the book?
2. In the expression 101 – 102 = 1 move just one digit or
character to make it correct. There are even two solutions
to this problem!
3. A three digit number starts with 7. By moving this digit to
the end, we get a new three-digit number which is smaller
than the previous number by 117. Which number is it?
4. Julie, Kate, Dave and Josh were picking cherries from a
tree. Julie collected most of all, Kate – not the least. Is it
true that the girls collected more cherries than the boys?
5. In the following sequence replace * with a number:
7, 17, 37, 77, *, 317, …
6. A boy was asked how many sisters and brother he has. His
answer was: “I have twice as many sisters as brothers”.
When a girl from the same family was asked the same
question she replied: “The number of my sisters is equal
to the number of my brothers”. How many boys and girls
are in this family?
7. The teacher places a sheet of paper with several circles
drawn on it in front of Andrew. “How many circles do you
see on this sheet”, the teacher asks. “Seven”, Andrew
answers. “Correct” says the teacher. Then he places the
same sheet of paper in from of Lillian and asks her the
same question. “Five”, answers Lillian. “Correct”, says the
teacher. How many circles are drawn on this sheet of
paper?
8. Daniel loves orange juice and he can drink a whole gallon
of it in 10 days. For his younger brother Nate it takes 2
weeks to drink a gallon of juice. How long will it take two
brothers to drink a gallon of juice if they drink from the
same container?
9. Mark several dots on the number line. Put another dot
between each two dots. Once more, put a dot in between
each two dots. Do the same for several more times. Prove
that after each such action the overall number of dots will
be odd.