Mario's Staircase

Algebra Level 1

In the image, King Bowser has used 10 blocks to build 4 of the steps to his castle. He makes sure that every step is exactly one block taller than the previous step.

How many blocks, in total, would he need to build a staircase of 10 steps?


The answer is 55.

Agnishom Chattopadhyay by Agnishom Chattopadhyay , 22, India

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4 solutions

Áron Bán-Szabó
Jul 12, 2017

The number of blocks we need is 1 + 2 + 3 + ⋯ + 10 = 11 × 10 2 = 55 1+2+3+\dots+10=\dfrac{11\times10}{2}=\boxed{55}

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Mohammad Khaza
Jul 23, 2017

look carefully,

first step is made of 1 brick

2nd step is made of 2 bricks

3rd step is made of 3 bricks

so, 10th step will be made of 10 bricks

so, the summation of bricks are=1+2+3+..........+10= 10 × 11 2 \frac {10 \times 11}{2} = 55 55

1 Helpful 0 Interesting 0 Brilliant 0 Confused

This is just triangle numbers. A very easy problem!

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Nikhil Raj
Jul 12, 2017

Number of blocks we require = ∑ n = 1 10 n = 1 + 2 + 3 + ⋯ + 10 = 55 \displaystyle \sum_{n = 1} ^{10} n = 1 + 2 + 3 + \dots + 10 =\boxed{55}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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