Olympiad problems from previous weeks

Below you will see the problems that have been posted in the hall, with the oldest one at the bottom.  


March 3

The sum of five consecutive whole numbers is 45.  


What is the smallest of the five numbers?


February 17


Jeff has some coins.  He can put the same number of coins into each of 9 bags with no coins left over.  He can put the same number of coins into each of 6 bags with no coins left over.   He can put the same number of coins into each of 5 bags with 2 coins left over.  


What is the smallest number of coins that Jeff could have?


February 3

A rectangle 4 cm by 12 cm is divided into four triangles, as shown.  The areas of the four triangles are stated in the picture.  Find the number of square cm in the area of the shaded triangle.
For every $3.00 Marisa spends, Andie spends $5.00.  


Andie spends $120.00 more than Marisa does.


How much does Andie spend?

November 11


How many different natural numbers will each leave a remainder of 5 when divided into 47?


Notes: A natural number is a positive, whole number (0, 1, 2, 3....)  If a child doesn't know where to start, it would be easy to count out 47 objects (cheerios, buttons, blocks, etc.) and actually move them into groups.

November 4


Thirty cubes are placed in a line such that they are joined face to face.  The edges of each cube are one cm long.  




Find the number of square cm in the solid surface area of the resulting solid.


Notes: For this one, it is important to think of the first cube, then think about two cubes together, then three.  Children were too quick to say "180!" because they multiplied 6 x 30.  But they were not thinking about the END parts.


October 28


If I start with 3 and count by 4’s until I reach 99, I get 3, 7, 11, … 99 where 3 is the first number, 7 the second number, 11 is the third number and so on.   


If 99 is the Nth  number, what is the value of N?


Notes: We are just beginning to use variables (in this problem, the variable is "N") labeled with letters, but I remind children they have been using them since they were small!  When we write "3 + ___ = 5", it is the same idea.




How many 2-digit numbers have an odd number as the sum of their digits?


Notes: For this problem, you need to be really clear about these terms:

sum: the answer to an addition problem

digit: any of the numerals 0 to 9

odd number: any number ending in 1, 3, 5, 7, or  9