**Que 16: There are 100 water bottles. One of the bottles contains poisoned water. If a rat drinks poisoned water he will die after one hour of it. You have 1 hour to find out which bottle has the poison. How many minimum rats are needed to figure out which bottle contains poison? Ans 16:** We can use digital logic to find out the poisoned bottle. Also, the rat will die in 1 hour and we have only 1 hour to figure it out we can give that water to rat only once. If we use the digital logic 100 numbers can be represented in 8 bits. If we convert each number into a digital number and give the water to those rats only if that position contains 1. Suppose the poison is in the 10

^{th}(00001010)bottle we will give the water to the 2

^{nd}and 4

^{th}rats. After 1 hour, we check which rats have died(represent logic 1) and which have not died(represent logic 0) and we can form back the number and we can figure it out. So, we need 8 rats to figure out the poisoned water bottle.

**Que 17: You have a box with 10 pairs of blue socks, 10 pairs of black socks, and 10 pairs of gray socks of the same size. You can pick one sock at a time. How many times do you have to pick the socks from the box to ensure that you have at least one pair of socks with the same color? Ans 17:** You have a total of 30 pairs of socks. If you pick 30 socks there might be a chance that all the socks are of the same leg. So, if we pick 1 more sock It will ensure that we will have a pair of socks. So we need to pick 31 socks from the box.

**Que 18: You have a rectangular sheet with a circular hole anywhere in the sheet, you know the center of the sheet and the center of the hole, How will you divide the sheet into two parts such that their areas are equal? Ans 18:** If we draw a straight line from the center of the rectangle in any direction it will divide the rectangle into 2 equal halves and the same in the circle. So we can draw a line that passes through the center of both rectangle and circle. This line will divide the sheet into two parts with equal area.

**Que 19: You have a balance scale, You need to measure integer weights from 1kg. to 40kgs. only. How many minimum numbers of weights do you need if you can put weights on one side of the scale? Ans 19:** We have weights that add up to 40 kg. we have 2 choices either we put it on balance or won’t put it. Hence, we can use binary weights which can count from 1 to 40. So the weights will be 2

^{0}, 2

^{1}, 2

^{2}, 2

^{3}, 2

^{4}, 2

^{5}which is 1, 2, 4, 8, 16, 32. A total of 6 weights are needed.

**Que 20: In the previous question, what is the minimum number of weights needed if you can put your weights on both sides of the scale. Ans 20:** In this question, we can put the weights on either side of the balance scale or don’t put them on the scale. So, you will have 3 options +1, 0, or -1. We can use base 3 combinations of the weights 3

^{0}, 3

^{1}, 3

^{2}, 3

^{3}which is 1, 3, 9, 27. A total of 4 weights are needed.

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