Question

One block is needed to make an up-and-down staircase, with one step up and one step down.

4 blocks make an up-and-down staircase with 2 steps up and 2 steps down.

How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
Explain how you would work out the number of blocks needed to build a staircase with any number of steps.
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Answer 1

Answer:

25

Step-by-step explanation:

One step up takes one block.

Two steps take four blocks.

Five steps take twenty-five blocks.

"A" steps will take "A"-squared blocks (A x A).

So the rule is any number of steps times itself equals the number of blocks you use.

The first time there is 1 block; 1 step up and 1 step down.

Then there are 4 blocks; 2 steps up and 2 steps down. Altogether the blocks equal 4. (3+1=4) Since 1 double is 2 and 3-1=2 we should try adding 2 each time. Then it would get to this ...

I

III

IIIII

IIIIIII

IIIIIIIII

This makes perfect sense because 1+3=4 which is the top two lines as 4 was the answer to the second time the blocks were built. 4+5=9. This one would be the third time. 9+7=16. 16 would be the fourth time. And lastly, 16+9=25.

The fifth time (which is the answer) would look like this on the form of steps...

   I              1

  III             3

 IIIII           5

IIIIIII          7

IIIIIIIII         9

This answer has five steps up and five steps down just like the question. That comes to the answer which is 25.