Problem No. 20 A cup of water

"Please give me a cup of water!"

You have a 7 cup bottle and a 30 cup bottle. How can you measure one cup of water?

Parent tip

You can make your own 7 cup and 30 cup bottles. Take two bottles, measure the wanted amount of water and mark the bottles, very carefully, at their maximal levels, the first one as the 7 cup bottle, and the other one as the 30 cup bottle. Then you can all have fun, you and your children, with pouring the water in and out of the bottles.

Problem No. 19. Divisibility

For which values of \(n\), is \(2n+5\) divisible by 7? And for which values, is it divisible by 30?

Student tip

Check with the reminders of \(n\) when dividing by 7. A number is divisible by 30, if it is divisible by 2, 3 and 5.

Problem No. 18. Min-max sum

What is the minimum and what is the maximum sum of 7 numbers which product is equal to 30?

Teacher tip

Suitable for exercising the factorization of numbers.

Problem No. 17. Cookies

There are 7 different types of cookies in Christine's Bakery that Mary loves. Mary wants to buy 30 cookies. If we suppose that there are enough cookies of each type she loves (at least 30 cookies of each type), in how many different ways can she buy her cookies?

Student tip

Recall how to count all possible ways to select items from a collection, such that the order of selection does not matter.

Problem No. 16. Points on a plane

7 different colors are used for coloring 30 points on a plane. Prove that, regardless the way you color them, there will always be at least five points colored in the same color.

Parent tip

You can enjoy a fun family time with your children coloring the points in different colors and different ways.