Difficult Mathematical Puzzles - 4

Q.1. A number of 5 digits have the following properties:

The number comprising the leftmost two digits is divisible by 2, that comprising the leftmost three digits is divisible by 3, the leftmost four by 4, the leftmost five by 5, . Each digit in the number is different i.e. no digits are repeated. The digit 0 does not occur in the number i.e. it is comprised only of the digits 5-9 in some order. How many such numbers are possible and find their value/values?.

Q.2. Power went off when Vijay was studying. It was around 2:00 AM. He lighted two uniform candles of equal length but one thicker than the other. The thick candle is supposed to last four hours and the thin one one hours less. When he finally went to sleep, the thick candle was twice as long as the thin one. For how long did Vinay study in candle light?

Q.3. Rohit kanwar went to hitbullseye bank to withdraw X rupees and Y paise from the bank. But cashier made a mistake and gave him Y rupees and X paise. Neither Rohit nor the cashier noticed that. After spending 23 paise, Rohit counts the money. And to his surprise, he has double the amount he wanted to withdraw. Find X and Y. (1 Rupee = 100 Paise)

Q.4. Find all sets of consecutive integers that add up to 1000.

Q.5. Lala Kirorimal's locker has a 5 digit number as the key. The 4th digit is 4 greater than the second digit, while the 3rd digit is 3 less than the 2nd digit. The 1st digit is thrice the last digit. There are 3 pairs whose sum is 11. Find the number.

As per given conditions, there are three possible combinations for 2nd, 3rd and 4th digits. They are (3, 0, 7) or (4, 1, 8) or (5, 2, 9). It is given that there are 3 pairs whose sum is 11. All possible pairs are (2, 9), (3, 8), (4, 7), (5, 6). Now the required number is a 5 digit number and it contains 3 pairs of 11. So it must not be having 0 and 1 in it. Hence, the only possible combination for 2nd, 3rd and 4th digits is (5, 2, 9). Also, 1st digit is thrice the last digit. The possible combinations are (3, 1), (6, 2) and (9, 3), out of which only (6, 2) with (5, 2, 9) gives 3 pairs of 11. Hence, the answer is 65292.

Q.6. Consider a number 268, where last digit is the sum of first two digits i.e. 2 + 6 = 8. How many such 3-digit numbers are there?

Q.7. There is a 50m long soldier’s unit advancing forward. The last individual in the unit desires to give a letter to the foremost person leading the unit. So while the unit is marching he runs to the front, reaches the foremost person and hands over the letter to him and without stopping, he runs and comes back to his original position. In the mean time the whole unit has moved ahead by 50m. How much distance did the last person cover in that time? Assume that he ran the whole distance with uniform speed.

Q.8. Ram says to Sham, "Can you figure out how many Eggs I have in my bucket?" He gives 3 clues to Sham: If the number of Eggs I have

I) is a multiple of 5, it is a number between 1 and 19

II) is not a multiple of 8, it is a number between 20 and 29

III) is not a multiple of 10, it is a number between 30 and 39

How many Eggs does Ram have in his bucket?

Q.9. There are four clustors of Oranges, Apricots and Bananas as follows:

Clustor I : 1 Orange, 1 Apricot and 1 Banana

Clustor II : 1 Orange, 5 Apricot and 7 Bananas

Clustor III : 1 Orange, 7 Apricots and 10 Bananas

Clustor IV : 9 Oranges, 23 Apricots and 30 Bananas

Clustor II costs Rs 300 and Clustor III costs Rs 390.

Can you tell how much does Clustor I and Clustor IV cost?

Solution & Explanation