## Preparation- Tear a piece of paper into nine (9) pieces about the same size.
- Write the digits 1 to 9 on the pieces, one on each piece of paper
- Write the title of this challenge and today's date on a fresh page in your maths journal.
## The Big ChallengeNow you have found three solutions. Are they really different? The answer to that depends on how you answer these questions.
## Digging Deeper- What happens if the cross arms are only three (3) squares and we use the digits 1 to 5?
*How many solutions are there?*(Perhaps none.)
*How will we know when we have found them all*. (If there are any.) - What happens if the cross arms are seven (7) squares and we use the numbers 1 to 13?
- If there are solutions for 5, 9, 13, ... arm crosses, is there a pattern in the minimum number of solutions as the cross gets bigger?
- Suppose we use the original cross and the digits 0 to 8. Are there any solutions?
- Let's do an experiment.
- Suppose all nine digits cards were placed face down and mixed around before they were put into a cross shape still face down.
- The experiment is that we turn them over to see if they are a solution to the Crosses puzzle.
- Suppose the experiment is done 30 times.
- What chance do you think there would be of a solution? 0 chances in 30, 1 chance in 30, 2 chances in 30, ...?
- Predict then carry out the experiment.
Note: If your school is a member of Maths300, your teacher can provide software that will help you explore Crosses.## Just Before You FinishRead your Working Like A Mathematician page again and answer this question in your journal.- What do you know now about Working Like A Mathematician that you didn't know before you started Crosses.
## Answers & DiscussionHints- Is there anything special about the middle number?
- Can all the nine digits be used in the middle?
- Suppose you put a digit that works into the middle. What has to be done with the other eight (8) digits?
- Does it help to know that the sum of the digits 1 to 9 is 45?
These photos from Year 4 at Homer Pittard School, Tennessee, show some of the solutions.
- Aaron Peeters Eritrea story.
- Notes for Crosses
Send any comments or photos about this activity and we can start a gallery here.
Maths At Home is a division of Mathematics Centre |