MATHS riddle

[abousoun]

Answer of The Crystal Soul's riddle:
let's consider :
x = amount of tomatoes
y = amount of given or offered tomatoes

first she had x
it rained --> 2x
saw J()e --> 2x - y
rained again 2(2x -y) = 4x - 2y
saw enigma --> 4x - 2y - y = 4x - 3y
rained again --> 2(4x-3y)= 8x - 6y
saw Sweets_HsN --> 8x - 6y - y = 8x - 7y
so the remaining is 8x - 7y which is equal to 0
8x - 7y = 0 --> 8x = 7y

The minimum values of x and y are 7 and 8 respectively to satisfy above equation
Hence, Crystal Soud had 7 tomatoes and she offered 8 tomatoes to each friend.

In general, Crystal Soul had 7N tomatoes initially and she offered 8N tomatoes to each friend, where N = 1, 2, 3, 4,

Winners : Crystal Soul, enigma

Thank You ...

[Crystal Soul]

Originally Posted by abousoun

Answer of the two numbers' riddle:
As Sweets_HsN is initially confident that they (i.e. he and Tawa) don't know the numbers, we can conclude that -
1) The sum must not be expressible as sum of two primes, otherwise Sweets_HsN could not have been sure in advance that Tawa did not know the numbers.
2) The product cannot be less than 12, otherwise there would only be one choice and Tawa would have figured that out also.
Such possible sum are - 11, 17, 23, 27, 29, 35, 37, 41, 47, 51, 53, 57, 59, 65, 67, 71, 77, 79, 83, 87, 89, 93, 95, 97, 101, 107, 113, 117, 119, 121, 123, 125, 127, 131, 135, 137, 143, 145, 147, 149, 155, 157, 161, 163, 167, 171, 173, 177, 179, 185, 187, 189, 191, 197, ....

Let's examine them one by one:
if the sum of two numbers is 11, Sweets_HsN will think that the numbers would be (2,9), (3,8 ), (4,7) or (5,6).

Sweets_HsN : "As 11 is not expressible as sum of two primes, Prashant can't know the numbers."
Here, the product would be 18(2*9), 24(3*8 ), 28(4*7) or 30(5*6). In all the cases except for product 30, Tawa would know the numbers.

- if product of two numbers is 18:
Tawa : "Since the product is 18, the sum could be either 11(2,9) or 9(3,6). But if the sum was 9, Sweets_HsN would have deduced that I might know the numbers as (2,7) is the possible prime numbers pair. Hence, the numbers must be 2 and 9." (OR in other words, 9 is not in the Possible Sum List).

- if product of two numbers is 24:
Tawa : "Since the product is 24, the sum could be either 14(2,12), 11(3,8 ) or 10(4,6). But 14 and 10 are not in the Possible Sum List. Hence, the numbers must be 3 and 8."

- if product of two numbers is 28:
Tawa : "Since the product is 28, the sum could be either 16(2,14) or 11(4,7). But 16 is not in the Possible Sum List. Hence, the numbers must be 4 and 7."

- if product of two numbers is 30:
Tawa : "Since the product is 30, the sum could be either 17(2,15), 13(3,10) or 11(5,6). But 13 is not in the Possible Sum List. Hence, the numbers must be either (2,15) or (5,6)." Here, Tawa won't be sure of the numbers.
Hence, Tawa will be sure of the numbers if the product is either 18, 24 or 28.
Sweets_HsN : "Since Tawa knows the numbers, they must be either (3,8 ), (4,7) or (5,6)." But he won't be sure. Hence, the sum is not 11.
Summerising data for sum 11:
Possible Sum....PRODUCT.....Possible Sum
2+9 ...................18............2+9=11 (possible)
3+6=9
3+8....................24........... 2+12=14
3+8=11 (possible)
4+6=10
4+7.................... 28............ 2+12=14
3+8=11 (possible)
4+6=10
5+6.................... 30............. 2+15=17 (possible)
3+10=13
5+6=11 (possible)

Following the same procedure for 17:
Possible Sum......... PRODUCT.......... Possible Sum
2+15...................... 30.................. 2+15=17 (possible)
3+10= 13
5+6=11 (possible)
3+14...................... 42................... 2+21=23 (possible)
3+14=17 (possible)
6+7=13
4+13...................... 52....................2+26=28
4+13=17 (possible)
5+12...................... 60....................2+30=32
3+20=23 (possible)
4+15=19
5+12=17 (possible)
6+10=16
6+11........................ 66..................2+33=35 (possible)
3+22=25
6+11=17 (possible)
7+10.........................70..................2 +35=37 (possible)
5+14=19
7+10=17 (possible)
8+9.......................... 72..................2+36=38
3+24=27 (possible)
4+18=22
6+12=18
8+9=17 (possible)

Here, Tawa will be sure of the numbers if the product is 52.
Sweets_HsN : "Since Tawa knows the numbers, they must be (4,13)."
For all other numbers in the Possible Sum List, Tawa might be sure of the numbers, but Sweets_HsN won't.

Here is the step by step explanation:
Sweets_HsN : "As the sum is 17, two numbers can be either (2,15), (3,14), (4,13), (5,12), (6,11), (7,10) or (8,9). Also, as none of them is a prime numbers pair, Tawa won't be knowing numbers either."
Tawa : "Since Sweets_HsN is sure that both of us don't know the numbers, the sum must be one of the Possible Sum List. Further, as the product is 52, two numbers can be either (2,26) or (4,13). But if they were (2,26), Sweets_HsN would not have been sure in advance that I don't know the numbers as 28 (2+26) is not in the Possible Sum List. Hence, the two numbers are 4 and 13."

Sweets_HsN : "As Tawa now knows both the numbers, out of all possible products - 30(2,15), 42(3,14), 52(4,13), 60(5,12), 66(6,11), 70(7,10), 72(8,9) - there is one product for which list of all possible sum contains ONLY ONE sum from the Possible Sum List. And also, no such two lists exist. [see table above for 17] Hence, two numbers are 4 and 13."

It is interesting to note that there are no other such two numbers. We (not me of course ) checked all the possible sums till 500!!!

Winners : No one answered correctly
Thank You ...

i wonder why

[Tawa]

Originally Posted by Crystal Soul

i wonder why

I Didn't Even Bother Myself Reading The Solution.

[abousoun]

A new Riddle (easy one) :
Tawa (after recovering from the car accident and buying a new one) drives his car to the university, he took 4 hours to reach the university since the wind was against him, on his way back home he took only 3 hours (here the wind was with his direction) ...

Assuming there is no wind, how much it will take him to reach home or university ? (mish fer2a raw7a aw raj3a since his university and home are on straight line)

Thank You ...

[abousoun]

Tawa submitted the first correct answer to the above riddle
why i have the feeling that everytime i post a riddle with someone's name , he will be the first one to solve it

Thank You ...

[Tawa]

Originally Posted by abousoun

Tawa submitted the first correct answer to the above riddle
why i have the feeling that everytime i post a riddle with someone's name , he will be the first one to solve it

Thank You ...

It Has To Do With The Instinct.

[abousoun]

Second winnder of the Tawa's car Riddle: Crystal Soul

Thank You ...

[abousoun]

Third winner Sweets_HsN

Thank You ...

[abousoun]

Answer of Tawa's Car Riddle:
Let distance between home and university is D. Tawa took 4 hours to reach university.
So speed while travelling towards university is D/4.
Similarly, he took 3 hours to reach home. So speed while coming back is D/3.
There is a speed difference of 7*D/12, which is the wind helping person in 1 direction, & slowing him in the other direction.
Average the 2 speeds, & you have the speed that person can travel
in no wind, which is 7*D/24. Hence, Tawa will take D / (7*D/24) hours to travel distance D which is 24/7 hours.
So the answer is 3 hours 25 minutes 42 seconds

Winners : Tawa, Crystal Soul, Sweets_HsN

Thank You ...

[abousoun]

New Riddle:
Find a number (A) in a way that if we moved the last digit and placed it at first ... we get a number (B) that's equal to 1.5 * (A)
example : (A) is abcde --> (B) will be eabcd ... and eabcd = 1.5(abcde)

Thank You ...