The numbers are 3 and 4. Ash has 7 and Maro has 12.
I'll try to explain to my best.
Both Ash and Maro would have some sets of numbers from the clue number they have got. Lets call Ash's sets of numbers as sum sets and Maro's sets as product sets.
So Sum sets starts from the number
4 - (2,2)
5 - (2,3)
6 - (2,4)(3,3)
7 - (2,5)(3,4)
8 - (2,6)(3,5)(4,4)
.
.
.
And Product sets start from the number
4 - (2*2)
6 - (2*3)
8 - (2*4)
9 - (3*3)
10 - (2*5)
12 - (2*2*3) - (2*6)(4*3)
14 - (2*7)
15 - (3*5)
16 - (2*2*2*2) - (2*8)(4*4)
18 - (2*3*3) - (2*9)(3,6)
.
.
.
Its obvious that both Ash and Maro are having more than a single set in their mind. Or else they can guess the number at very beginning itself. So we can omit all single set numbers.
Maro's first statement is "Ah, i knew you wouldn't be able to do this.". This means Maro also cant find the answer and he is sure that Ash also couldnt make it.
So Maro has a number with all its product sets tends Ash also have more than one set.
Maro's minimum number which can have two sets is 12. So we consider that Maro is having 12.
It have two sets - (2*6)&(4*3). These two sets if summed will come - 8 and 7. Maro is considering the possibilities of Ash. For both 8 and 7, Ash would have more than one set of numbers. So he is sure that Ash couldnt make the right numbers. But still Maro is not sure about which product set is right one. So he makes his first statement.
Now consider if Ash is having 8. which leads to the sets (2,6)(3,5)(4,4). He will consider the product sets of these sets
(2*6=12)(3*5=15)(4*4=16). All these product sets have multiple sets of Maro. SO Ash cant guess the number at this point if he have 8.
But after hearing Maro's first statement, Ash is able to find the numbers.
So lets now consider the other option that Ash is having 7, which leads the sum sets (2,5)(3,4). The product sets of these numbers are (2*5=10)(3*4=12). No Ash would think in his way that, if Maro has 10 which has only one product set(2,5), he would have guessed the number before making his first statement. But he hadnt. So he has the number 12.
And so, now Ash can determine that numbers were 3 and 4. And he says so.
Already, we assumed Maro is having 12 and so, now he will think in this way. As Ash had found the numbers, they could not be (2,6), because their sum is 8 and Ash knows sum sets of 8 will tends multiple options for Maro, SO Ash could not be sure about the numbers after Maro's first statement. But if Ash got 7, he can guess the numbers. So Maro decides Ash got 7. And so the numbers were 3 and 4.
I think this is right answer and enough explanation.
17th November 2008, 04:33 PM
Re: Can you guess the numbers?
Linear Mode
