Q1. How many squares in the following diagram ?
A1. Total squares 1 + 4 + 9 + 16 + 25 = 55 squares.

Figure

Q2. What is the definition ?
A2. Answer

• As diagram defining size-1 square
• The size-2 square including 4 size-1 squares : 1^2 + 2^2
• The size-3 square including 4 size-2 and 9 size-1 : 1^2 + 2^2 + 3^2

Q4. Why size-3 square can trace four size-2 squares ?
A4. From this diagram can you see the reason.

Q6. How many squares can be traced as shown in 1st diagram ?

Q7. Other number Square pattern

• 1 .... 4 ........ 9 ......... 16
  
  * .. * * .... * * * .... * * * *
  .... * * .... * * * .... * * * *
  ............. * * * .... * * * *
  ........................ * * * *
  

Q8. Formula : Sum[n^2] = n*(n+1)*(2*n+1)/6
A8. Four proof methods are given in Math Room