Month: October 2023

1. Here are 10 straight lines and 17 squares. What are the dimensions of the biggest square?

2. Can you draw another shape that makes 17 squares?

3. Here are 9 straight lines and 20 squares. Can you find all of the squares?

For the following questions only use rectanglular shapes (including square shapes):

4. Can you draw another shape that makes 20 squares?

5. How many different ways can you make 5 squares?

6; How many different ways can you make 14 squares?

7. How many different ways can you make 15 squares?

By thinking about what happens when you add a row and what happens when you add a column can you …

8. Find the smallest number of straight lines needed to make 30 squares.

9. Find the smallest number of straight lines needed to make exactly 100 squares.

You are given two lives to guess my number (which is between 1 and 100 inclusive).

If you guess too high you lose a life.

For example …

I’m secretly thinking of the number 42. If you guess 50 you lose a life. If you then guess 45 you lose your final life and you have failed.

After guessing 50 and losing a life you would then have to guess 1, guess 2, guess 3 and so on until you correctly guess 42. So this would work but would take a long time.

What strategy should you use to minimise the number of guesses it takes to guess my number? And what is the worst case scenario for how many guesses it could take?

If you are familiar with the two eggs problem it is essentially the same puzzle!