Question 1: Correct Addition

You can remove a digit from all three lines of this 4-digit addition, close up the gaps by moving digits to the right and … still leave a correct addition.

You can do the same with the 3-digit addition that remains and with the 2-digit addition, leaving a correct single-digit addition.

What are the correct 3-digit, 2-digit and 1-digit additions that remain at each stage?

Question 2: All in a Triangle

Our diagram shows three yellow and three blue balls fitting snugly into a triangle.

The Challenge

How many different patterns can the six balls make?

Now, we know that you will want to be clear about what we mean by different. So, let’s agree that you can’t just rotate or reflect (flip) a pattern to make it different. For example, this is what the original pattern looks like after rotation or reflecting and we’ll agree that all three count as being the same.

Question 3: Numbers in Boxes

The numbers 1 – 7 have been placed in each part of a diagram made with four boxes. The total of the numbers in each box is also shown ... and clicking on the box will open an applet that you might find helpful.

The First Challenge

How can the numbers be placed so that the numbers in each box add to a common total? What different common totals can be made?

The Second Challenge

How can the numbers be placed so that the totals in the boxes are consecutive numbers?

There are different solutions to this as well … if you have time to find them!