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Probability Level 2

How many squares do you see?

The answer is 1240.

2 solutions

U Z
Nov 10, 2014

Number of $1 cm^{2}$ squares from any corner is $1\times1 = 1^{2}$

Number of $2 cm^{2}$ squares from any corner is $2\times2 = 2^{2}$

Number of $15 cm^{2}$ squares from any corner is $15 \times 15 = 15^{2}$

Total = $1^{2} + 2^{2} + ................... 15^{2} = \frac{15.16.31}{6} = 1240$

we will not multiply it by 4 since we have covered all the area.

I did it by this way.

The total number of squares in this $15\times 15$ grid is $15\times 15 + 14\times 14 + 13\times 13 + 12\times 12 + 11\times 11 + 10\times 10 +9\times 9 + 8\times 8 + 7\times 7 + 6\times 6 + 5\times 5 + 4\times 4 +3\times 3 + 2\times 2 + 1\times 1$ which is equal to $\boxed{1240}$ @megh choksi

Anuj Shikarkhane - 6 years, 7 months ago

Yes its same @Anuj Shikarkhane

U Z - 6 years, 7 months ago

No. of 1 cm squares from any corner is 15×15 not 1×1.

No. of 15 cm squares from any corner is 1×1 not 15×15.

PUSHPESH KUMAR - 6 years, 7 months ago

I mean to say of area $1 cm^{2}$ . Thank you big mistake edited

U Z - 6 years, 7 months ago

Awesome!

I appreciate your solution.

Ninad Akolekar - 6 years, 6 months ago

Fox To-ong
Feb 18, 2015

Using binomial theorem for (2n+1)(n+1)n/(6)

Test your brain!

The answer is 1240.

2 solutions

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