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What was the problem?
Let's first recall the given equation.
BASE +
BALL
---------
GAMES
----------
We are assuming repeating the numbers are not allowed.
Let's first take last 2 digits operation into consideration i.e. SE + LL = ES or 1ES (carry in 2 digit operation can't exceed 1). For a moment, let's assume no carry generated.
10S + E + 10L + L = 10E + S .....(1)
9 (E - S) = 11L
To satisfy this equation L must be 9 and (E - S) must be equal to 11. But difference between 2 digits can't exceed 9. Hence, SE + LL must have generated carry.So rewriting (1),
10S + E + 10L + L = 100 + 10E + S
9 (E - S) + 100 = 11L
Now if [9 (E - S)] exceeds 99 then L must be greater than 9. But L must be digit from 0 to 9. Hence, [9 (E - S)] must be negative bringing down LHS below 100. Only value of E - S to satisfy the given condition is -5 with L = 5. Or we can say, S - E = 5.
Now, possible pairs for SE are (9,4), (8,3), (7,2), (6,1), (5,0). Out of these only (8,3) is pair that makes equation SE + LL = SE + 55 = 1ES i.e. 83 + 55 = 138. Hence, S = 8 and E = 3.
Replacing letters with numbers that we have got so far.
1
---------
BA83 +
BA55
---------
GAM38
----------
Now, M = 2A + 1. Hence, M must be odd number that could be any one among 1,7,9 (since 3 and 5 already used for E and L respectively).
If M = 1, then A = 0 and B must be 5. But L = 5 hence M can't be 1
If M = 7, then A = 3 or A = 8. If A = 3 then B = 1.5 and that's not valid digit. And if A = 8 then it generates carry 1 and 2B + 1 = 8 again leaves B = 3.5 - not a perfect digit.
If M = 9, then A = 4 (A = 9 not possible as M = 9) and B must be 7 with carry G = 1.Hence for first 2 digits we have 74 + 74 + 1 = 149.
Finally, rewriting the entire equation with numbers replacing digits as -
1
---------
7483 +
7455
---------
14938
----------
So numbers for letters are S = 8, E = 3, L = 5, A = 4, B = 7, M = 9 and G = 1.
There are five men, let's say Tarun, Harish, Lavesh, Manoj and Manish.
All of them have a dot mark in their forehead. They can't see the dot on
their own forehead, but can see the ones on others. The owner of WHITE
dot is an honest person and will never lie, while the owner of BLACK dot
always tell the lie.
This are the statement from Tarun, Harish, Lavesh, and Manish:
Tarun: 'I see 3 whites and 1 black'
Harish: 'I see 4 black'
Lavesh: 'I see 3 black and 1 white'
Manish: 'I see 4 white'
What color is the dot on each Tarun, Harish, Lavesh, Manoj, Manish forehead?
Know color of dot on each forehead!
Source
Read this story first!
Let's take a look at who said what.
Tarun: 'I see 3 whites and 1 black'
Harish: 'I see 4 black'
Lavesh: 'I see 3 black and 1 white'
Manish: 'I see 4 white'
Harish and Manish made very contracting statements; so are statement of Tarun and Lavesh. That means, only one of them is telling the truth. Hence, only one of 4 have WHITE dot on his forehead. Till now we don't have idea of what Manoj had on his forehead. Even if he has WHITE dot then there can be maximum 2 WHITE dots among those 5.
Truth of Tarun and Manish:
Tarun and Manish must be lying as they are saying that they have seen 3 and 4 WHITE dots respectively. According to our first conclusion, there can be maximum 2 WHITE dots possible.
Truth of Harish:
Next if we assume Harish has WHITE dot and telling the truth then all other must be lying including Manoj and Lavesh. As per Lavesh, he had seen 3 BLACK and 1 WHITE dot. Now he must have seen BLACK dots on foreheads of Manoj, Tarun, Manish and WHITE dot on forehead of Harish as assumed. That mean he is telling truth though he has BLACK dot. But the man with BLACK is always lying, hence this case is also INVALID.
Truth of Lavesh:
So the only person left is Lavesh and must be telling the TRUTH with WHITE dot on his forehead. Hence, as his statement is suggesting, the Manoj must have WHITE dot and other three Tarun, Lavesh, Harish have BLACK dots (we already concluded these 3 are lying).
