Maths Riddles

Total number of matches that are to be played are:
9C2 * 2
= 9! / (2!7!) * 2
= 8 * 9
= 72
And thus each team will play 16 matches.

Now let us examine the possible cases.

Case 1:
If suppose, Team A, Team B and Team C wins 14 matches each i.e. they lose 1 match each from the other two teams, then the Team D can win only 16 - 3 * 2 = 10 matches.

Case 2:
Now let us suppose if the top four teams win 13 matches each.
Team A: 13 wins and 3 loses from Team B, Team C and Team D.
Team B: 13 wins and 3 loses from Team A, Team C and Team D.
Team C: 13 wins and 3 loses from Team A, Team B and Team D.
Team D: 13 wins and 3 loses from Team A, Team B and Team C.

In this case, the Team E can only win a maximum of 8 matches as Team A, Team B, Team C and Team D will win all the matches played by E.

Case 3:
If suppose the top five team wins 12 matches each.
Team A: 12 wins and 3 loses from Team B, Team C, Team D and Team E.
Team B: 12 wins and 3 loses from Team A, Team C, Team D and Team E.
Team C: 12 wins and 3 loses from Team A, Team B, Team D and Team E.
Team D: 12 wins and 3 loses from Team A, Team B, Team C and Team E.
Team E: 12 wins and 3 loses from Team A, Team B, Team C and Team D.

Now Team E wins 12 matches but it still won't be able to qualify for the playoffs (assuming that it has the lowest run rate).

Therefore from case 2, it can be said that a team must win at least 13 matches to be sure to play in the playoffs.

There are 20 spokes in the given wheel.
360/S = A
360/(S +10) = A - 6

Let us use equations to solve this puzzle.

Rabbit + Cat = 10 Kg ---- Eq. 1
Dog + Rabbit = 20 Kg ---- Eq. 2
Cat + Dog = 24 Kg ---- Eq. 3

Now add all the three equations

2(Cat) + 2(Dog) + 2(Rabbit) = 10 + 24 + 24
2 (Cat + Dog + Rabbit) = 54
Cat + Dog + Rabbit = 27.

8

for b in range(1,99):
for g in range(1,99):
sum1=2*b*g+42
sum2=(b+g)*(b+g+1)
if(sum1==sum2):
print(b,g,sum1)

(b,g)=(3,5) => b + g=8

54

This problem is much simple than it appears to be. Just see to the fact that it will take 3 hours for the friends to meet. How? Go figure out with Speed, Distance and Time relations. Now, he dog will be running for three hours in total at 18 MPH. Thus he will cover a total distance of 18 * 3 = 54 miles.

101

(50 * 50 + x)/51 = 51
=>2500 + x = 51 * 51
=> x = 2601 - 2500
=> x = 101 (Answer)

Let us solve this question one step at a time.
We know that each time the ball is dropped it bounces back and reach 2/3 of the height.
Thus, after the first bounce, the ball will reach 2/3 of the height from which it was dropped.
After the second bounce, the ball will reach 2/3 of the height again after the first bounce.
Thus the total height at which the ball must have reached by this time will be 2/3 * 2/3 = 4/9 of the original height.
After third bounce, 2/3 * 2/3 * 2/3 = 8/27 of the original height.
After fourth bounce, 2/3 * 2/3 * 2/3 * 2/3 = 16/81 of the original height.


Thus, the ball will reach 16/81 of the original height from which it was dropped.

A cone comprises of exactly two surfaces despite of the fact that it is a three dimensional figure.

As you can see in the picture, this is how you must cut the board and join them to cover the hole completely without leaving any gap.

40 minutes

Total players = 8 + 6 = 14
Now, the question has told us that only eight players are present on the field at one time.
70 * 8 = 560 min in total.
Now dividing that with 14, we can conclude that each player was there on the pitch for 40 minutes (560/14)