Mathematical Puzzles form an essential part of many competitive exams. One of the most commonly asked questions is based on arithmetic puzzles. Another important type of question features in form of number puzzles. Here is a compilation of the various types of medium-level mathematical puzzles with answers and explanations. Each article features a set of 10 math brain teasers to evaluate your level of preparation.

Practice these mathematical puzzles and check your aptitude:

Q.1. In a swimming competition that went on for n successive days (n>1), m medals were awarded.

medal and 1/9 of the remaining (m – 1) medals were awarded on the first day.

medals and 1/9 of the now remaining medals was awarded on the second day; and so on.

The remaining n medals were awarded, on the nth and last day.
If same number of medals were awarded daily, how many days did the contest last, and how many medals were awarded altogether?

Total 64 medals were awarded and the contest was for 8 days.
On day 1: Medals awarded = (1 + 63/9) = 8 : Remaining 56 medals
On day 2: Medals awarded = (2 + 54/9) = 8 : Remaining 48 medals
On day 3: Medals awarded = (3 + 45/9) = 8 : Remaining 40 medals
On day 4: Medals awarded = (4 + 36/9) = 8 : Remaining 32 medals
On day 5: Medals awarded = (5 +27/9) = 8 : Remaining 24 medals
On day 6: Medals awarded = (6 + 18/9) = 8 : Remaining 16 medals
On day 7 : Medals awarded = (7 + 9/9) = 8 : Remaining 8 medals
On day 8, the remaining 8 medals are awarded

Q.2. There is banana shake in yellow colored glass and apple juice in a white colored glass, both containing equal volumes of shake and juice. 100ml of banana shake is taken and poured into the white glass. After that similarly, 100 ml from the white glass is poured into the yellow glass. Of the two quantities, the amount of apple juice in the yellow glass and the amount of banana shake in the white glass, which one is greater and by how much?

The two quantities are equal.
Let's assume that both glasses contain 900 ml of liquid each. Now, 100ml of the banana shake is taken and poured into the White glass. Hence, yellow colored glass contains 800 ml of banana shake and white glass contains 900 ml of Apple juice and 100 ml of banana shake i.e. total of 1000 ml. Similarly, 100 ml of juice from white glass is poured into yellow glass. Now this 100 ml is not a pure apple juice. It contains 90 ml of apple juice and 10 ml of banana shake. Hence, yellow glass contains 810 ml of banana shake and 90 ml of Apple juice. Similarly, white glass contains 810 ml of apple juice and 90 ml of banana shake.
Now it is clear that the amount of apple juice in the yellow glass and the amount of banana shake in the white glass are the same.

Q.3. A positive integer that, when added to 2000 gives a sum which is greater than when multiplied by 2000. Find the positive integer.

The positive integer is 1.
Sum of 1 and 2000 = 1 + 2000 = 2001
Multiplication of 1 and 2000 = 1 * 2000 = 2000
Thus, sum of 1 and 2000 is greater than the multiplication of 1 and 2000.

Q.4. I was inquisitive and asked Mr. Dhaliwal about his birthday. With a mischievious smile on his face he replied. "The day before yesterday I was 96 years old and next year I will be 99." Assume that the current year is 2010, can you figure out the date of birth of Mr. Dhaliwal? .

Mr. Dhaliwal's date of birth is 31 December, 1912
Today is 1 January, 2010. The day before yesterday was 30 December, 2009 and Mr. Dhaliwal was 96 on that day. Today i.e. 1 January, 2010 - he is 97. On 31 December 2010, he will be 98 and next year i.e. 31 December, 2011 - he will be 99. Hence, the date of birth is 31 December, 1912.

Q.5. Everyday in his business Prakash had to weigh amounts from 1 kg to 364 kgs, to the nearest kg. What is the minimum number of different weights required and how heavy should they be?

The minimum number is 6
They should weigh 1, 3, 9, 27, 81 and 243 kgs.

Q.6. If Kumbkaran eats 60 pounds of rice every day EXCEPT every 7th day on which he only eats 50 pounds of rice. If he continues this, how many pounds of rice will he eat in 150 days?

It is given that on every 7th day he eats 50 pounds of rice i.e. on day number 7, 14, 21, 28, .... 140, 147 kumbkaran eats 50 pounds of rice.
Total number of 7th days = 150/7 = 21 ( he eats 50 pounds)
Hence, the normal days are = 150 - 21 = 129 ( he eats 50 pounds)
Thus, in 150 days, he will eat
= (129) * (60) + (21) * (50)
= 7740 + 1050
= 8790 pounds

Q.7. Which of the following set would contain the most 4's that when added together will sum the most ?
999 - 778, 777 - 556 or 555 - 333?

555-333
As the numbers 400 401 402 ......499 .. will contain 100 4's more than other set .

Q.8. You have a balance and the following weights: 4kg, 8kg, 16kg, 32kg, and 64kg. How many different possible weights can you measure with these items?

Start with a weight of 4kg and notice what happens on doubling the weight (4,8,16,32,64). (Here, "0 kg" is included as a weighing for a purpose)
4kg: can weigh 0kg or 4kg (2 possibilities)
4kg and 8kg: can weigh 0kg or 4kg or 8kg or 12kg (4 possibilities)
4kg, 8kg and 16kg: can weigh 0kg or 4kg or 8kg or 10kg or 12kg or 20g or 24g or 28kg (8 possibilities)
It doubles each time!
So with 4 weights there are 16 possibilities.
And with 5 weights there are 32 possibilities.
Now, since we have added "0 grams" only for checking the pattern, therefore just subtract one, for an answer of 31.

Q.9. 2 crates are being used to carry six boxes. Each crate can carry a maximum of 50 kg. The total weight of the boxes is 100kg:
30 kg, 26kg, 20 kg, 16 kg, 4 kg, 4kg,
In how many different ways can these boxes be packed into the crates?

Two cases are possible:
30, 20 26, 16, 4, 4
16, 30, 4 20, 26, 4

Q.10. Mr. Sahil runs the Bulls Eye Bank.
You have to help him, though, because he has forgotten the combination number of the safe of the bank. Fortunately, he does remember some things about the number which may help you to help him.

The number has four digits (eg.1234 or 9876).

All the digits are different.

It begins and ends with an odd number and has two even numbers in the middle.

19 and 519 divide it exactly.

What is the number which will open the safe?

The combination number of Mr. Sahil's bank safe is 9861.
A bit of a trick puzzle, really, because out of the four clues, the last one alone gives you the answer: Since 19 is not a factor of 519, therefore, the code for safe has to be a multiple of 19 as well as 519. Thus, just multiply 519 x 19 and you get 9861. The other clues are just for checking the answer.