Question 1: Bags of Marbles

This picture shows the number of marbles in each bag.

 Alice, Brie and Charlie each have three bags of marbles. Alice has 26 marbles and Brie has 21 marbles. Charlie doesn’t have the bag with 9 marbles in it.

Question

Who had which bags of marbles

Question 2: With Four Squares

Part 1

What different shapes can be made with 4 squares that are joined along at least one edge?

Part 2

How can you use the shapes that you found in Part 1 to cover this 4 by 4 grid if these rules are followed.

Rules

1. No two shapes are allowed to overlap.
2. No shapes are allowed to stick out over the edge of the grid.
3. The shapes used do not have to be different.
4. The numbers covered by each shape must add to the same total.

Question 3: On See-through Paper

If you write the numbers 1 to 9 on a strip of see-through paper you can make it into a ring.

Then you can make a list of the numbers that you see starting at any number on the ring. For example, if you start on 5, your list will be:

5, 6, 7, 8, 9, 1, 2, 3, 4.

Now, take a strip of see-through paper and divide it into eleven positions.

Going left to right, put your list of numbers onto the strip, filling the shaded places first and then use the last three numbers to put into positions A, B and C.  For example, with the above list, your strip would look like this and you would have made three numbers 546, 738 and 921.

If you turn your strip over and read the numbers in mirror writing, then you would have made the three numbers 129, 837 and 645.

The Challenge

There are two lists of numbers that you make from your ring which produce three numbers with the following property:

The difference between the smallest number and the middle number is the same as the difference between the middle number and the largest number.

What are those lists and do they work (i.e. have the same property) when you turn your strip over?