#1: (From Mathcounts handbook) Find more information on Mathcounts here -- the best middle school math competition program up to the national level.
16-page booklet is made from a stack of four sheets of paper that is
folded in half and then joined along the common fold. The 16 pages are
then numbered from front to back, starting with page 1. What are the
other three page numbers on the same sheet of paper as page 5?\
Solution: It’s always a good idea to simplify a question when it’s totally new and see if you can find the pattern.
Fold a sheet of paper in half and mark the page numbers: 1-2-3-4
have you got? Page 1 is always followed by page 2, page 3 by page 4…..
When page numbers increase, it follows the same pattern, so page 77 will be followed by page 78, etc…
thing to notice is on the same side, page 1 is opposite of page 4 and
page 2 is opposite of page 3. 1 + 4 = 5 The same goes to 2 + 3 Now we
can solve this problem.
Since this is a 16-page
booklet, page 1 will be opposite of page 16, so the sum of the numbers
on the same side will all equal to 17.
Page 5 will be followed by
page 6. The opposite number of page 5 would be 17 – 5 = 12 and the
number opposite 6 would be 17- 6= 11
The answer is 6, 11, and 12.
(Online brainteaser): The girls in gym class today sat around a large
circle and spaced themselves evenly. The gym teacher asked them to count
aloud in order, starting with 1, 2, 3, and so on. When they were
finished counting, the girl who was 21st was sitting directly across
from the girl who was 7th. How many girls were sitting around the
Again simplify the question. Let’s make it 6 girls. In this case 1 will
be opposite 4 and 2 will be opposite 5, 3 will be opposite 6.
do we get 6 girls? Observe the number pairs and you will see if you
multiply the difference by 2, you’ll get 6 each time. 2 (4-1) = 2(5-2) =
So the answer to the question would be 2(21-7) = 28