Eyes of 2nd Doraemon is different

ANSWER-
37, 397, 3997, 39997, 399…..997 etc.

As
37 * 2 – 1 = 73
397 * 2 – 1 = 793
399….997 * 2 – 1 = 799….993

EXPLANATION-
Method to find the number,
We first try to find the possible number which consist of two digits.

Let the number be x , such that x = AB (where A and B are two digits)

In other words, x = 10 * A + B,
It holds that 2 * x – 1 = 20*A + 2*B – 1

If we reverse this number, we’ll get the original number AB back.
But then it of course also hold that if you reverse the original number (that becomes 10 * B + A), you will get 20*A + 2*B – 1.

Therefore,
20 * A + 2 * B – 1 = 10 * B + A

We can equate this as-
19 * A = 8 * B + 1.

The right hand side of this equation is always odd and hence the left part should be odd as well.
This implies that A should be odd.
The right part is always smaller than 73.

So A cannot be larger than 3.
If we try A = 1,
we do not find a solution.

But A = 3 has a solution with B = 7.
So the number we search for is 37. This is the only number with two digits that satisfies our requirements.

From oldest to youngest the sisters are:

The seating arrangement is:

———- Dad ———-
Hank              –           Danica
Christie        –            Ian
Kyle                –            Farrah
Electra          –            Edward
Michael        –            Brooke
Gabrielle     –            James
Lars                –            Angelina
———- Mom ———-

BONUS ANSWER 😛
The year is 2003. This is the only year from 2000 to 2007 where Christmas is on a Thursday.

Both are same as A and B are the same person.

EXPLANATION-
As it is mentioned that 500 men are arranged in an array of 10 rows and 50 columns according to their heights.
Let’s assume that position numbers represent their heights.
Hence,
the shortest among the 50, 100, 150, … 450, 500 is person with height 50 i.e. A. Similarly the tallest among 1, 2, 3, 4, 5, ….. 48, 48, 50 is person with height 50 i.e. B

Now, both A and B are the person with height 50.
Hence both are same.

Both A and B are of the same height.

Because,
when we arange the matrix in increasiong order we get 50 is the shortest among each row and 50 is the the tallest among shortest from each column.

Answer – Total 4 persons (including you) required.

EXPLANATION-
It is given that each person can only carry enough rations for five days and as there are 4 persons.
Hence, total of 20 days rations is available.

1. Day 1 : 4 days of rations are used up. One person goes back using one day of rations for the return trip. The rations remaining for the further trek is for 15 days.

2. Day 2 : The remaining three people use up 3 days of rations. One person goes back using 2 days of rations for the return trip. The rations remaining for the further trek is for 10 days.

3. Day 3 : The remaining two people use up 2 days of rations. One person goes back using 3 days of rations for the return trip. The rations remaining for the further trek is for 5 days.

4. Day 4 : The remaining person uses up one day of rations. He stays overnight. The next day he returns to the coast using 4 days of rations.

Thus, total 4 persons, including you are required.

 The total numbers of zeroes required are
= 11 + (8*20) + 21
= 11 + 160 + 21
= 192

Hence, 192 zeros will be required.

Answer – 6

EXPLANATION-
Looking at the diagram in rows,
The central circle equals half the sum of the numbers in the other circles to the left and right of the centre.

Answer – “O” must be placed in the center.

EXPLANATION-
Let’s number the positions as:
1 | 2 | 3
———
4 | 5 | 6
———
7 | 8 | 9

It is given that “X” is placed in one of the corner position. Let’s assume that its at
position 1.

Now, let’s take each position one by one.

• If “O” is placed in position 2, “X” can always win by choosing position 4, 5 or 7
• If “O” is placed in position 3, “X” can always win by choosing position 4, 7 or 9
• If “O” is placed in position 4, “X” can always win by choosing position 2, 3 or 5
• If “O” is placed in position 6, “X” can always win by choosing position 3, 5 or 7
• If “O” is placed in position 7, “X” can always win by choosing position 2, 3 or 9
• If “O” is placed in position 8, “X” can always win by choosing position 3, 5 or 7
• If “O” is placed in position 9, “X” can always win by choosing position 3, or 7

So, By placing “O” at the center i.e. 5 by player 2, Player 1 can never win

Step 1 : First, fill the 5 liter jug and then pour it into the 3 liter jug. The 5 liter jug now has only 2 liters left.

Step 2 : Next, empty out the 3 liter jug. Then, pour the 2 liters from the 5 liter jug to the 3 liter jug. So, now the 3 liter jug has 2 liters.

Step 3 : Fill the 5 liter jug again, and pour 1 liter into the 3 liter jug. Now,  exactly 4 liters is present in 5 liters jar!

jug1   jug2
5           3
5           0  Pour from Jar1 to Jar2
2           3
2           0  Empty jar 2
0           2 Pour from Jar1 to Jar2
5           2 Pour from Jar1 to Jar2 – Only 1 liter can be poured 
4           3 ———— 4 Liter —— left in jar1