Problem No. 24. Three friends

Who is lying?

Ann says "Mine watch is showing 7.30." Betty says "Mine and Ann's watches are showing 7.30." Cintia says "Mine or Betty's watches are not showing 7.30." Only one of three friends is lying. Which one could be lying? If you are allowed to chose, which watch will you want to see, to be certain who is lying?

Teacher tip

Use occasionally logic puzzles to exercise students' logical reasoning.

Problem No. 22. Lines on a plane

Let's draw lines!

Is it possible that 7 lines on a plane have 30 intersection points in total? Can they have twenty intersection points?

Student tip

Find the maximum number of intersection points. Start with two lines, add one at a time, until you reveal the pattern.

Problem No. 21. Missing numbers again

Here is a new brain teaser!

Find the missing numbers, if the tables follow the same rule.

6	17	2		3	21	1
8		22				12
5	13			6	9	4

Teacher tip

Brain teasers can be used as "worm ups" at the beginning of the class.

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. 15. Jenn's blog

Jenn has a blog site. She started blogging on July 30 at 7.30 am. She is posting her posts at exactly 7 hours and 30 minutes apart. When will she post her 730th post?

Teacher tip

Suitable for practicing calendar calculations.

Problem No. 12. Sum of squares

Find all representations of the number 730 as a sum of two squares? And as a sum of three squares?

Teacher tip

Suitable for implementing the elimination and reminder methods while practicing the square numbers up to \(30^2\).

Problem No. 9. Points on a circle

How many points can be drawn on a circle such that each two adjacent points are at the same distance, and each three adjacent points form an angle of \(7^o 30'\).

Student tip

You need to recall on the properties of inscribed angles in a circle.

Problem No. 8. Seven 7s

How can you make 30, using seven 7s and the basic math operations (brackets are allowed)? What is the smallest number of 7s you can use, to make 30?

Parent tip

Have fun with your kids by exploring and calculating different number sentences. Do not forget that the brackets can help a lot.

Problem No. 7. Coins on a table

There are 7 coins laid on a table with the heads up, and 30 coins laid with the tails up. Each coin has a head side and a tail side. How can you split the coins in two piles, with your eyes closed, so that the piles have the same number of coins with the tails up?

Teacher tip

Use logic puzzles at your classes to increase the motivation and to exercise the flexibility in mathematical thinking.

Problem No. 6. Clock hands revisited

How many times in a day the clock hands will form the same angle as the angle at 7.30?

Student tip

For a hint use Problem No. 3.

Problem No. 5. Missing numbers

Here is a 5 x 5 table filed with numbers according to some rule. What are the missing numbers?

Parent tip

Exploring patterns with your children can be a fun way to spend some quality time together.

Problem No. 3. Clock hands

It is 7.30 now. How much time will it pass until the clock hands form the same angle again?

Student tip

Suppose that minute and hour hands move at a constant velocity each.