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With the help of “Getting Started”, I worked out the number of blocks needed for the different number of steps up to 4 steps as follows:-

Number of steps Number of blocks needed
1 1
2 4
3 9
4 16

Then I observed a pattern with the numbers in the column “number of blocks needed”. The number of blocks needed is the square of the number of steps (the number times the same number).

Number of steps Number of blocks needed Pattern
1 1 1 x 1 = 1
2 4 2 x 2 = 4
3 9 3 x 3 = 9
4 16 4 x 4 = 16

So the number of blocks needed to build an up-and-down staircase with 5 steps up and 5 steps down is 25 (5 times 5).

Number of steps Number of blocks needed Pattern
1 1 1 x 1 = 1
2 4 2 x 2 = 4
3 9 3 x 3 = 9
4 16 4 x 4 = 16
5 25 5 x 5 =25

In this way, we can work out how many blocks are needed to build an up-and-down staircase with a bigger number of steps.