Solution:

19

Explanation:
The Cost of 1st Wizard is: 50 i.e Total coins spend: 50
The Cost of 2nd Wizard is: 100 i.e Total coins spend: 150
The Cost of 3rd Wizard is: 150 i.e Total coins spend: 300
The Cost of 4th Wizard is: 200 i.e Total coins spend: 500
The Cost of 5th Wizard is: 250 i.e Total coins spend: 750
The Cost of 6th Wizard is: 300 i.e Total coins spend: 1050
The Cost of 7th Wizard is: 350 i.e Total coins spend: 1400
The Cost of 8th Wizard is: 400 i.e Total coins spend: 1800
The Cost of 9th Wizard is: 450 i.e Total coins spend: 2250
The Cost of 10th Wizard is: 500 i.e Total coins spend: 2750
The Cost of 11th Wizard is: 550 i.e Total coins spend: 3300
The Cost of 12th Wizard is: 600 i.e Total coins spend: 3900
The Cost of 13th Wizard is: 650 i.e Total coins spend: 4550
The Cost of 14th Wizard is: 700 i.e Total coins spend: 5250
The Cost of 15th Wizard is: 750 i.e Total coins spend: 6000
The Cost of 16th Wizard is: 800 i.e Total coins spend: 6800
The Cost of 17th Wizard is: 850 i.e Total coins spend: 7650
The Cost of 18th Wizard is: 900 i.e Total coins spend: 8550
The Cost of 19th Wizard is: 950 i.e Total coins spend: 9500
The cost of 20th Wizard is: 1000 i.e Total coins spend: 10500 .... more than 10,000.

Solution:

Align the toothpicks to form TEN. Use one toothpick for each of the lines.

Solution:

I will be thrown at lions. Now if Akbar threw him at lions, Birbal’s statement will stand true and he will have to bury him alive. But if he bury him, the statement will emerge as false. Thus he had no choice left

Solution:

The competition was held on 11 November 2013. The logic is simple. In America, the dates are mentioned as Month/Day/Year and in Britain, dates are written as Day/Month/Year. But on 11 November 2013, the date and month will be the same. And thus both will write in the same manner i.e. 11/11/2013. If it would have been any other date, the evaluators would have been able to identify it.

Solution:

For this answer is 3^0, 3^1, 3^2... That is 1,3,9,27,81,243 and 729.

Solution:

He should draw any chit of paper and before unfolding it, he must eat and swallow the chit. In this manner, to determine the judgment of the god, they will have to look at the other chit which will have 'Guilty' written over it. Thus everyone will believe that the chit which he ate had innocent written over it and thus they will believe that he is innocent.

Solution:

TIF56

Explanation:
The password is formed as:
T (5th letter of Shruti)
I (5th letter of Arshika)
F(1st letter of Friday)
5(5th day of week)
6(Length of Friday)

Similarly, we will pick the 1st letter for Monday and 3rd letter for Wednesday.

Solution:

A typical way will be to start thinking about summing up the distance that the bee will travel but that will be quite a tedious task. How about we offer you a much easy solution?

The tunnel is 200 miles long and the trains are running at as peed of 100 mph which means that they will collide exactly at the center of the tunnel and seeking their speed, they will collide after an hour.

Now consider the bee which is flying at a speed of 1000 mph and will keep flying till the train collides. As calculated, it will keep flying for an hour which means the distance that it will cover is 1000 miles.

Solution:

73

Explanation:
It's a very famous puzzle known as "Josephus Problem Puzzle". It can be solved in various ways but the trick to solve this problem is illustrated below.

Binay number of 100 is: 1100100
complement pf 100 is 0011011, whose decimal equivalent is 27.
The desired answer will be 100 - 27 = 73

Solution:

The check was for dollars 31.63.

The bank teller gave her dollars 63.31
She spent .05, and then she had dollars 63.26, which is twice the check.

Let x be the dollars of the check, and y be the cent.

The check was for 100x + y cent
He was given 100y + x cent

Also
100y + x - 5 = 2(100x + y)
Expanding this out and rearranging, we find:
98y = 199x + 5

or 199x ≡ -5 (mod 98)
or 98*2*x + 3x ≡ -5 (mod 98)
3x ≡ -5 ≡ 93 (mod 98)
this quickly leads to x = 31

Solution:

Firstly: Policeman should take the thug across the river thames and escort the boat back with him. (Thug across, everyone else on this side)
Then, Policeman will take one cat along, leave it there, and on the way back, bring back the thug (since thug cannot be left with anyone without policeman's supervision).
Then Mrs. Mother will take the second cat on the other side. Drop it there and bring the boat back. For the 4th trip, Mrs. Mother And Mr. Father Will travel to the other side, and Mrs. Mother will stay there, and MR. Father will bring the boat back. (Now Mrs. Mother and 2 cats are on the other side.)
5th trip, the policeman takes the thug across. Both of them stay there and Mrs. Mother will come back. Then for the next trip, Mr. Father and Mrs. Mother will go on the boat, and Mrs. Mother will stay there, and Mr. Father will return back.
Then for the 7th trip, Mr. Father will travel with one dog. On the return, the policeman and the thug will return. Then in the next trip, the Policeman will take the second dog. (Now Mrs. Mother and her two cats; Mr. Father and his two dogs and the Policeman is here).
Now finally the policeman takes the boat on the other side and brings back the thug.
Tough one, right ?