Mathematics puzzle games enhance your brain power and memory. These are based on the basic concepts of algebra, arithmetic, ratio & proportion, probablity etc. Here, we have compiled some of the best math riddles according to their level of difficulty. Each article contains a set of 10 puzzle questions with solutions. In this article, you will come across medium level maths number puzzles with answers and explanations.
Solve these puzzles related to maths and check your mental aptitude:
Q.1. For her Birthday, Madhuri Dutt bought some T-shirts. If she gives 6 T-shirts to each friend, one friend will get only 4 T-shirts. Also, if she gives 4 T-shirts to each friend, she will have 30 T-shirts remaining. How many T-shirts she got on her Birthday, and how many friends are there?
Let's assume that there are total T T-shirts and F friends.
According to first case, if she gives 6 T-shirts to each friend, one friend will get only 4 T-shirts.
6*(F - 1) + 4 = T
Similarly, if she gives 4 T-shirts to each friend, she will have 30 T-shirts remaining.
4*F + 30= T
Solving above 2 equations, F = 16 and T = 94. Hence, Madhuri got 94 T-shirts and 16 friends.
Q.2. Punkhuri and Chiriya met each other after a long time. In the course of their conversation, Punkhuri asked Chiriya her age. She replied, "If you reverse my husband's age, you will get my age and he is older than me. Also, the sum of our ages is 11 times the difference of our age." Can you help out Punkhuri in finding Chiriya's age?
Assume that Chiriya's age is 10X+Y years. Hence, her hubby's age is (10Y + X) years.
It is given that difference between their ages is 1/11th of the sum of their age.
Hence, the possible values are X=4, Y=5 and Chiriya's age is 45 years.
Q.3. A fish had a tail as long as its head plus a quarter the length of its body. Its body was three-quarters of its total length. Its head was 4 inches long. What was the length of the fish?
It is obvious that the length of the fish is the summation of lengths of the head, the body and the tail. Hence, Fish (F) = Head (H) + Body (B) + Tail (T)
But it is given that the length of the head is 4 inches i.e. H = 4. The body is three-quarters of its total length i.e. B = (3/4)*F.
And the tail is its head plus a quarter the length of its body i.e.
T = H + B/4.
Thus, the equation is
F = H + B + T
F = 4 + (3/4)*F + H + B/4
F = 4 + (3/4)*F + 4 + (1/4)*(3/4)*F
F = 8 + (15/16)*F
(1/16)*F = 8
F = 128 inches
Thus, the fish is 128 inches long.
Q.4. In a temple, there were three beggars. A pilgrim came to the temple with few coins. The pujari of the temple gave him a magic bag in which coins get doubled each time you put that coins into it. He put all the coins he had in that bag and the coins got doubled. He took out all the coins and gave few to the first beggar and then again put the remaining coins back in the bag. The coins got doubled again; he took out all the coins again and gave few coins to the second beggar. He then again put the remaining coins in the bag and the coins got doubled again. He took out all the coins and gave few coins to third beggar. There were no coins left with him when he gave coins to third beggar and he gave equal number of coins to each beggar. What is the minimum number of coins the pilgrim had initially? How many coins did he gave to each beggar?
Assume that the pilgrim had X coins initially and he gave Y coins to each beggar.
From the above figure, there are (8X - 7Y) coins left with pilgrim after giving coins to third beggar. But it is given that there were no coins left with him at the end. It means that (8X - 7Y) = 0, so we get 8X = 7Y.
The minimum values of X and Y are 7 and 8 respectively to satisfy above equation. Hence, the pilgrim had 7 coins and he gave 8 coins to each beggar. In general, the pilgrim had 7N coins initially and he gave 8N coins to each beggar, where N = 1, 2, 3, 4, .....
Q.5. There is a grid of 20 squares by 10 squares. How many different rectangles are possible? Note that square is a rectangle.
Total number of rectangles = (Summation of row numbers) * (Summation of column numbers)
Here there are 20 rows and 10 columns or vice versa. Hence, total possible rectangles
Q.6. A man took a certain number of apples to the bazaar and sold some of them. The next day, through the orchid of his apples, the number left over had been doubled, and he sold the same number as the previous day. On the third day the new remainder was tripled, and he sold the same number as before. On the fourth day the remainder was quadrupled, and his sales the same as before. On the fifth day what had been left over were quintupled, yet he sold exactly the same as on all the previous occasions and so disposed of her entire stock. What is the smallest number of apples he could have taken to market the first day, and how many did he sell daily? Note that the answer is not zero.
Let's assume that he had N apples on the first day and he sold X apples everyday. Putting down the given information in the table as follows:
Apples at the start of the day
N – X
It is given that he disposed of his entire stock on the fifth day. But from the table above, the number of apples remaining are (120N-206X).Hence,
120N - 206X = 0
120N = 206X
60N = 103X
The smallest value of N and X must be 103 and 60 respectively. Hence, he took 103 apples to market on the first day and sold 60 apples everyday.
Q.7. Jagdish and Vishnu are playing cards for a stake of Re.1 a game. At the end of the evening, Jagdish has won 3 games and Vishnu has won Rs.3. How many games did they play?
They played total of 9 games. Jagdish won 3 games and Vishnu won 6 games.
If Jagdish has won three games and Vishnu has won Rs.3, he lost a rupee for each loss, therefore he has won 6 and lost 3 to make Rs.3 and won the other 3 that he lost!
Q.8. A baaz, an eagle, is flying between two trains, each travelling towards each other on the same track at 60 km/h. Baaz reaches one engine, reverses itself immediately, and flies back to the other engine, repeating the process each time. Baaz is flying at 90 km/h. If the Baaz flies 180 km before the trains meet, how far apart were the trains initially?
The baaz is flying at the speed of 90 km/h and covers 180 km. Hence, the Baaz flies for 2 hours after trains started. It's obvious that trains met 2 hours after they started travelling towards each other. Also, trains were travelling at the speed of 60 km/h. So, each train traveled 120 km before they met. Hence, the trains were 240 km apart initially.
Q.9. How many squares are there in a 5 cm by 5 cm square lattice? Note that the lattice is made up of one cm by one cm squares.
There are 25 squares of 1 cm by 1cm.
There are 16 squares 2 cm by 2 cm
There are 9 squares of 3 cm by 3 cm
There are 4 squares of 4 cm by 4 cm
There is 1 square of 5 cm by 5 cm
Hence, there are total 25 + 16 + 9 + 4 + 1 = 55 squares.
For a lattice of N by N, the possible number of squares is = N2 + (N - 1)2 + (N - 2)2 + ......... + 32 + 22 + 12
Q.10. Sagrika multiplied 414 by certain number and obtained 69958 as the answer. But she found that there is some error in the answer - both the 9s in the answer are wrong and all the other digits are correct. Can you find the correct answer?
The correct answer is 60858.
If you divide 69958 by 414, you will get 168.98. Hence, assume some three digit number and multiply it by 414 and use 6**58 as the answer. It is obvious that the last digit of the assumed number must be 7.
* * 7
x 4 1 4
* * 8
* * 7 0
* * 8 0 0
6 * * 5 8
Now, the second last digit of the assumed number must be 4 or 9. Also, the first digit of the assumed number must be 1 as the first digit of the answer is 6. Using trial and error for above two conditions, the answer is 60858.