Answer / guest

The numbers are 4 and 13.

As Sachin is initially confident that they (i.e. he and
Prashant) don't know the numbers, we can conclude that -

1) The sum must not be expressible as sum of two primes,
otherwise Sachin could not have been sure in advance that
Prashant did not know the numbers.

2) The product cannot be less than 12, otherwise there would
only be one choice and Prashant 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, Sachin will think that the
numbers would be (2,9), (3,8), (4,7) or (5,6).

Sachin : "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, Prashant
would know the numbers.

- if product of two numbers is 18:

Prashant : "Since the product is 18, the sum could be either
11(2,9) or 9(3,6). But if the sum was 9, Sachin 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 otherwords, 9 is not in the Possible Sum List)

- if product of two numbers is 24:

Prashant : "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:

Prashant : "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:

Prashant : "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, Prashant won't be sure of the numbers.

Hence, Prashant will be sure of the numbers if product is
either 18, 24 or 28.

Sachin : "Since Prashant 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, Prashant will be sure of the numbers if the product is
52.

Sachin : "Since Prashant knows the numbers, they must be
(4,13)."

For all other numbers in the Possible Sum List, Prashant
might be sure of the numbers but Sachin won't.

Here is the step by step explaination:

Sachin : "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, Prashant
won't be knowing numbers either."

Prashant : "Since Sachin 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), Sachin 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, two
numbers are 4 and 13."

Sachin : "As Prashant 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."

Nakul figured out both the numbers just as we did by
observing the conversation between Sachin and Prashant.

It is interesting to note that there are no other such two
numbers. We checked all the possible sums till 500 !!!

An orange colored glass has Orange juice and white colored glass has Apple juice both of equal volumes. 50ml of the orange juice is taken and poured into the white glass. After that similarly, 50ml from the white glass is poured into the orange glass. Of the two quantities, the amount of apple juice in the orange glass and the amount of orange juice in the white glass, which one is greater and by how much?

5 Answers   marketRx,

---

if 12+22=24 23+8=6 32+13=40 73+16=144 then 36+2=? explain

13 Answers   Hawkins, Infosys, L&T, Reliance, TCS, Total, Wipro,

---

a is person take 10 days to do a work, b is a person take 15 days to do same work, if both do the work how many days will they take

7 Answers   Infotech,

---

rich man keeps me in pocket, poor men throws me away, children eat me, am a tamil word _u_ _e_ _l

9 Answers   Adama Agricultural Solutions, Infosys, Mannar Company, Wipro,

---

why do you want to work here?

1 Answers   Qatar Airlines,

---

x^y+y^x=5298.If x and y are integers find x and y.

1 Answers  

---

1)PORK/CHOP = C,IF C=2 FIND PORK AND CHOP??? 2)ATOM + BOMB = BINGO.IF A=7 and G= 9, find ATOM BOMB BINGO.

6 Answers   Godrej,

---

1 bird ko fish se pyar ho gaya. wo dono mile to kaise? fish paani ko chhod nahi sakti aur bird paani me ja nahi sakta.

5 Answers   Syscon,

---

what is Next number in the series is 1 , 2 , 4 , 13 , 31 , 112 , ?

10 Answers   Infosys,

---

Five students - Akash, Chintan, Jignesh, Mukund and Venky - appeared for an exam. There were total five questions - two multiple choice (a, b or c) and three true/false questions. They answered five questions each and answered as follow. I II III IV V -------------------------------------------------- Chintan c b True True False Akash c c True True True Jignesh a c False True True Mukund b a True True False Venky b b True False True -------------------------------------------------- Also, no two students got the same number of correct answers. Can you tell which are the correct answers? What are their individual score?

1 Answers  

---

A number of 9 digits has 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, and so on for the nine digits of the number i.e. the number formed from the first n digits is divisible by n, 2<=n<=9. ? 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 1-9 in some order. Find the number.

1 Answers  

---

Submit Answer Users Answer (48) BrainVista Answer Puzzle A Friend Add to Favourite Back to Search Result Hello sajeesh murali ? my Answers ? my Favourites ? Modify Personal Info ? Subscribe ? Logout ? Jigsaw Puzzle ? Join the Dots ? Marbles Game ? Balls Game ? Towers of Hanoi ? Think Number ? Find A Day Brain Teaser No Three Gold (G) coins, three Silver (S) coins and three Copper (C) coins are arranged in a single row as follow: G S C G S C G S C ? Only 2 adjacent unlike coins can be moved at any one time. ? The moved coins must be in contact with at least one other coin in line. i.e. no pair of coins is to be moved and placed away from the remaining ones. ? No coin pairs can be reversed i.e. a S-C combination must remain in that order in its new positionwhen it is moved. What is the minimum number of moves required to get all the coins in following order? C C C S S S G G G Show all moves.

1 Answers  

---