Amazing Math Puzzles With Answers 1 : Probability Riddle Loaded Revolver
Difficulty ★★☆☆☆ Popularity ★★★★★ Henry has been caught stealing cattle, and is brought into town for justice. The judge is his ex-wife Gretchen, who wants to show him some sympathy, but the law clearly calls for two shots to be taken at Henry from close range. To make things a little better for Henry, Gretchen tells him she will place two bullets into a six-chambered revolver in successive order. She will spin the chamber, close it, and take one shot. If Henry is still alive, she will then either take another shot, or spin the chamber again before shooting.
Henry is a bit incredulous that his own ex-wife would carry out the punishment, and a bit sad that she was always such a rule follower. He steels himself as Gretchen loads the chambers, spins the revolver, and pulls the trigger. Whew! It was blank. Then Gretchen asks, 'Do you want me to pull the trigger again, or should I spin the chamber a second time before pulling the trigger?'
What should Henry choose?
Answer & Explanation
Solution:
Henry should have Gretchen pull the trigger again without spinning.
We know that the first chamber Gretchen fired was one of the four empty chambers. Since the bullets were placed in consecutive order, one of the empty chambers is followed by a bullet, and the other three empty chambers are followed by another empty chamber. So if Henry has Gretchen pull the trigger again, the probability that a bullet will be fired is 1/4.
If Gretchen spins the chamber again, the probability that she shoots Henry would be 2/6, or 1/3, since there are two possible bullets that would be in firing position out of the six possible chambers that would be in position.
Difficulty ★★☆☆☆ Popularity ★★★☆☆ Lavesh can paint a a house in just 3 hours.However it takes 6 hours for vishesh to complete the same job.
How long would it take for both to complete the same job?
Answer & Explanation
Solution:
two hours.
lavesh who could complete the job in 3 hours could complete 2/3 of the job in two hours. Vishesh who complete the job in 6 hours could complete 1/3 of the job in two hours.
2/3 + 1/3 = 1.
Difficulty ★★★★☆ Popularity ★★★★★ Two old friends, Jack and Bill, meet after a long time.
Three kids
Jack: Hey, how are you man?
Bill: Not bad, got married and I have three kids now.
Jack: That"s awesome. How old are they?
Bill: The product of their ages is 72 and the sum of their ages is the same as your birth date.
Jack: Cool..But I still don"t know.
Bill: My eldest kid just started taking piano lessons.
Jack: Oh now I get it.
How old are Bill"s kids?
Answer & Explanation
Solution:
3,3,8
Lets break it down. The product of their ages is 72. So what are the possible choices?
2, 2, 18 sum(2, 2, 18) = 22
2, 4, 9 sum(2, 4, 9) = 15
2, 6, 6 sum(2, 6, 6) = 14
2, 3, 12 sum(2, 3, 12) = 17
3, 4, 6 sum(3, 4, 6) = 13
3, 3, 8 sum(3, 3, 8 ) = 14
1, 8, 9 sum(1,8,9) = 18
1, 3, 24 sum(1, 3, 24) = 28
1, 4, 18 sum(1, 4, 18) = 23
1, 2, 36 sum(1, 2, 36) = 39
1, 6, 12 sum(1, 6, 12) = 19
The sum of their ages is the same as your birth date. That could be anything from 1 to 31 but the fact that Jack was unable to find out the ages, it means there are two or more combinations with the same sum. From the choices above, only two of them are possible now.
2, 6, 6 sum(2, 6, 6) = 14
3, 3, 8 sum(3, 3, 8 ) = 14
Since the eldest kid is taking piano lessons, we can eliminate combination 1 since there are two eldest ones. The answer is 3, 3 and 8.
Difficulty ★★★☆☆ Popularity ★★★★★ Baseball bat and ball cost $50. If the bat cost $49 more than the ball, what is the cost of each
Answer & Explanation
Solution:
bat $49.50, ball $0.50
Difficulty ★★★☆☆ Popularity ★★★★★ I drive at an average speed of 30 miles per hour to the railroad station each morning and just catch my train. On a particular morning there was a lot of traffic and at the halfway point I found I had averaged only 15 miles per hour. How fast must I drive for the rest of the way to catch my train?
Answer & Explanation
Solution:
The train is just about to leave the station and there is no way I will be able to catch it this time.
Difficulty ★★★☆☆ Popularity ★★★☆☆ Can you get a sum of 1000 using sixteen 4s and only an addition operator
Answer & Explanation
Solution:
444 + 444 + 44 + 44 + 4 + 4 + 4 + 4 + 4 + 4 = 1000
Difficulty ★★★★☆ Popularity ★★★★☆ At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?
Answer & Explanation
Solution:
12
In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n.
Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66.
This is the quadratic equation n2+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.
Since 66 is a relatively small number, you can also solve this problem with a hand calculator. Add 1 + 2 = + 3 = +... etc. until the total is 66. The last number that you entered (11) is n.
Difficulty ★★★★☆ Popularity ★★★☆☆ Can you find a seven digit number which describes itself. The first digit is the number of zeros in the number. The second digit is the number of ones in the number, etc. For example, in the number 21200, there are 2 zeros, 1 one, 2 twos, 0 threes and 0 fours.
Answer & Explanation
Solution:
3211000
==============================================Amazing Math Puzzles With Answers 9 : Maths Equation Puzzle
Difficulty ★★★★☆ Popularity ★★★☆☆ I know a way by which i can make i can get total of 120 by using five zeros 0,0,0,0,0 and any one mathematical operator.
Do you ?
Answer & Explanation
Solution:
(0!+0!+0!+0!+0!)!
=(1+1+1+1+1)!
=(4)!
=5! is 5*4*3*2*1=120
Difficulty ★★★★☆ Popularity ★★★★☆ A women walks into a bank to cash out her check.
By mistake the bank teller gives her rupee amount in change, and her paise amount in rupees.
On the way home she spends 5 paise, and then suddenly she notices that she has twice the amount of her check.
How much was her check amount ?
Answer & Explanation
Solution:
The check was for Rupees 31.63.
The bank teller gave her Rupees 63.31
She spent .05, and then she had Rupees 63.26, which is twice the check.
Let x be the rupees of the check, and y be the paise.
The check was for 100x + y paise
He was given 100y + x paise
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
