**Que 11: Calculate the number of squares in an 8×8 chessboard. ****Ans 11:** To calculate the number of squares in an 8×8 chessboard, we will calculate first with smaller numbers like 2×2 and 3×3.

In 2×2 there will be 4+1 = 5 squares.

In 3×3 there will be 9+4+1 = 14 squares.

In 4×4 there will be 16+9+4+1 = 30 squares.

Following the pattern we can calculate for 8×8 chessboard will be 64+49+36+25+16+9+4+1 = **204**

**Que 12: you have a 3 liter and a 5 liters buckets (Assume unlimited water source available). How will you measure 4 liters of water. Ans 12:** We can follow the below sequence to get 4 liters of water. We can make the combination of 5 + 5 – 3 – 3 = 4 ltr. Refer to Table 6 for the sequence of activity.

**Que 13: Find the angle between the minute and hour hands of the clock at 4:20 PM. Ans 13:** First calculate the position of the minute hand w.r.t. 12 o’clock at 20 min. = (20*360

^{o}/60) = 120

^{o}. Then we can calculate the position of hour hand w.r.t 12 o’clock at 4:20 PM, we can write it as 4

_{20/60}= 4

_{1/3}=

^{13/3}. To convert into the angle (13/3×360

^{o}/ 12 ) = 130

^{o}. The Angle formed by the hour and minute hand will be

**10**.

^{o}**Que 14: You have two sand timers, which can show 4 minutes and 7 minutes respectively. Use both the sand timers(at one time or one after another or any other combination) and measure a time of 9 minutes.****Ans 14: **Start the 7-minute sand timer and the 4-minute sand timer.

Once the 4-minute sand timer ends turn it upside down instantly.

Once the 7-minute sand timer ends turn it upside down instantly.

After the 4-minute sand timer ends turn the 7-minute sand timer upside down(it has now a minute of sand in it) So effectively 8 + 1 = 9.

**Que 15: You have 9 balls, 8 of which have the same weight. The remaining one is defective and heavier than the rest. You can use a balance scale to compare weights to find which is the defective ball. How many measurements do you need so that you will be surely able to do it? Ans 15:** We can split the balls into 3 groups with 3 balls in each group. Then we can compare any 2 groups if they are equal then defective ball is in the 3rd group or it will be in the heavier group. Then we will get 3 balls in which 1 is heavier, again we can compare 2 balls if they are equal 3rd ball is defective else heavier ball. So, in total, we need to measure 2 times to find out heavier balls.