Change the number into a special number.

$132$

Check whether the given number is special number or not.

$273$

Take any number. Now multiply it by $2,3,4,......$ at every step. Also, add $3$ to it at each step. Look at the difference in the answer. Is it the same at every step?

$$\begin{gathered} 12\times 2+3=27 \\ 12\times 3+3=39 \\ 12\times 4+3=51 \\ 12\times 5+3=63 \\ 12\times \_\_+3=\_\_ \\ \_\_\times 7+3=\_\_\_ \\ \_\_\_\times \_\_\_+3=\_\_\_ \\ \_\_\_\times \_\_\_\times \_\_\_=\_\_\_ \end{gathered}$$ 

Look at the numbers below. Look for the pattern. Can you take it forward?

$$\begin{gathered} \left(9-1\right)÷8=1 \\ \left(98-2\right)÷8=12 \\ \left(987-3\right)÷8=123 \\ \left(9876-4\right)÷8=\_\_\_\_\_ \\ (98765-5)÷8=\_\_\_\_\_ \\ ( - )÷8=\_\_\_\_\_ \\ ( - )÷8=\_\_\_\_\_ \end{gathered}$$

$$\begin{gathered} 1+2+3+4+5+6+7+8+9+10=55 \\ 11+12+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+20=155 \\ 21+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+30=\_\_\_\_\_ \\ 31+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+40=\_\_\_\_\_ \\ 41+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+50=\_\_\_\_\_ \\ 51+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+60=555 \\ 61+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+70=\_\_\_\_\_ \end{gathered}$$

Did you notice some pattern in the answers?

Take the first two odd numbers. Now add them, see what you get.
Now, at every step, add the next odd number.

$$\begin{gathered} 1+3=4=2\times 2 \\ 1+3+5=9=3\times 3 \\ 1+3+5+7=16=4\times 4 \\ 1+3+5+7+9=\_\_\_\_\_=\_\_\_\_\_\times \_\_\_\_\_ \\ 1+3+5+7+9+11=\_\_\_\_\_=\_\_\_\_\_\times \_\_\_\_\_ \\ 1+3+5+7+9+11+13=\_\_\_\_\_=\_\_\_\_\_\times \_\_\_\_\_ \end{gathered}$$

Banno and Binod were playing a guessing game by writing clues about a secret number. Each tried to guess the other’s secret number from the clues. Can you guess their secret number?

• It is larger than half of $100$
• It is more than $6 \mathrm{tens}$ and less than $7 \mathrm{tens}$
• The tens digit is one more than the ones digit
• Together the digits have a sum of $11$.

Banno and Binod were playing a guessing game by writing clues about a secret number. Each tried to guess the other’s secret number from the clues. Can you guess their secret number?

• It is smaller than half of $100$.
• It is more than $4 \mathrm{tens}$ and less than $5 \mathrm{tens}$.
• The tens digit is two more than the ones digit.
• Together the digits have a sum of $6$.

Take any number and double it now multiply the result by $5$ and then finally divide the answer by $10$. Find the surprise number.