MATHS riddle

[Tawa]

Originally Posted by abousoun

J()e, Sweets_HsN and Tawa were gathered together in a network place ...
Suddenly J()e byo5tor 3ala belo 2 numbers and then says "fakkart bi ra2mein majmou3on ... " w bi5abbir Sweets_HsN bi majmou3on only

byirja3 bi2oul "if i multiply both numbers the result will be ..." w bi5abbir Tawa bil result only

so Sweets_HsN bi2oul : "5ayye Tawa ma bzon 7a na3rif hal 2 numbers"
Tawa replies : "ahhhhhhhhhh, halla2 3reft el numbers wez 3aynak "
Sweets_HsN : "yiiiiiiiiii, kamena ana 3refton hehehehehe "

Can you figure out these 2 numbers ?

Important Notes :
1 - these 3 guys are math geeks ... ya3ne ktirrrrr zakeya w byikmshouha 3al tayir
2 - each one concluded something from the other's statement
3 - the 2 numbers are > 1

Thank You ...

One Question: Do I Know About The Note?
I Mean, Do Tawa And Sweets_HSN Knows That Both Numbers Are Greater Than 1?

[abousoun]

Originally Posted by Tawa

One Question: Do I Know About The Note?
I Mean, Do Tawa And Sweets_HSN Knows That Both Numbers Are Greater Than 1?

yes you are math genious, you concluded something from Sweets_HsN comment and you already know that the number is above 1

Thank You ...

[Sogelec]

Originally Posted by abousoun

yes you are math genious, you concluded something from Sweets_HsN comment and you already know that the number is above 1

Thank You ...

Kteeer 5ateera hal Riddle

I Know There is Somethin Here

so Sweets_HsN bi2oul : "5ayye Tawa ma bzon 7a na3rif hal 2 numbers"
Tawa replies : "ahhhhhhhhhh, halla2 3reft el numbers wez 3aynak "
Sweets_HsN : "yiiiiiiiiii, kamena ana 3refton hehehehehe "

[J()e]

abousoun pm sent mafroud tkoun sa7

and abt the switch riddle

mnekbos 2awal kabse,,we wait 10 mins and the mnkebos tene kabse
we leave the room w mnrou7 3a 2oudit el lamba 3 2e7timelet:
1-iza el lamba mdoweye->el kabse el makbouse is the correct one
2-iza el lamba motfiyeh...mndessa,iza kenit 7emye ya3ne el kabse li kabasneha 2awal chi hieh el sa7
3-iza el lamba motfiyeh w mish 7emyeh-> el kabse li ma kabasneha hiyeh el sa7

[Tawa]

Originally Posted by J()e

abousoun pm sent mafroud tkoun sa7

and abt the switch riddle

mnekbos 2awal kabse,,we wait 10 mins and the mnkebos tene kabse
we leave the room w mnrou7 3a 2oudit el lamba 3 2e7timelet:
1-iza el lamba mdoweye->el kabse el makbouse is the correct one
2-iza el lamba motfiyeh...mndessa,iza kenit 7emye ya3ne el kabse li kabasneha 2awal chi hieh el sa7
3-iza el lamba motfiyeh w mish 7emyeh-> el kabse li ma kabasneha hiyeh el sa7

What's The Second Solution?

[Crystal Soul]

i do'nt think that there's any other solution
yalla badna news riddles , abousoun's riddle ma ela 7al

[abousoun]

Crystal Soul was carrying a bag of tomatoes ... while she was walking, it started to rain a little bit and to her surprise the amount of tomatos doubled in her bag !!!!
then it stopped raining, and saw J()e on the corner who was very hungry, so she gave small amount of Tomatoes ...

then she continued her way back to home, again it started to rain, and the amount of remaining tomatoes doubled again ...
after the rain stopped, she continued her way home and encountered enigma who was desperate for some tomatoes to make tabboule, so Crystal Soul gave her small amount of tomatoes as well ...

then it started to rain again (what a crazy day !!! ), and the remaining amount of tomatoes doubled in her bag too ... after stoppage of rain, she saw Sweets_HsN who was in need of tomatoes because he wanted to throw them on sanioura's car ... so she gave him small amount of tomatoes too ...

When Crystal Soul reached home, she noticed she didn't have anymore tomatoes w akalita bahdale min emma

can you figure out the smallest amount of tomatoes that Crystal Soul had initially? and how much tomatoes she gave to J()e, enigma, Sweets_HsN ? (taking into consideration that she gave all 3 of them the same amount)

Thank You ...

[abousoun]

Crystal Soul first one to solve the above riddle
yalla chabeb cheddo el hemme ... this shouldn't take more than 2 minutes maximum .... 1 minute for solving and 1 minute for writing pm

Thank You ...

[abousoun]

enigma the second one to solve the Crystal Soul's riddle
today i'll post the answers of both riddle, this one and the two numbers riddle

Thank You ...

[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 ...