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What was the challenge?
We need only 7 trips to send all digits across the river.
1. Send 2, 5, 9 (sum is 16).
2. Bring back the 9.
3. Send 3,4, 9 (sum is 16).
4. Bring back the 9.
5. Now send 1,7,8 (sum is 16).
6. Bring back the 1.
7. And finally send 1,6,9 (sum is 16).
A prisoner is faced with a decision where he must open one of two doors. Behind each door is either a lady or a tiger. They may be both tigers, both ladies or one of each.
If the prisoner opens a door to find a lady he will marry her and if he opens a door to find a tiger he will be eaten alive. Of course, the prisoner would prefer to be married than eaten alive :).
Each of the doors has a statement written on it. The statement on door one says, “In this room there is a lady, and in the other room there is a tiger.”
The statement on door two says, “In one of these rooms there is a lady, and in one of these rooms there is a tiger.”
The prisoner is informed that one of the statements is true and one is false.
Which door should the Prisoner open?
This should be his choice!
What were the choices?
For a moment, let's assume that first statement is true. The lady is behind the Door 1 and tiger is behind the Door 2. But this makes statement 2 also true where it says there is tiger behind one of these door & lady behind one of these doors. Hence, the statement 1 can't be true.
Hence, statement 2 must be true.
Only possibilities left are -
Door 1 - Tiger
Door 2 - Tiger
Door 1 - Lady
Door 2 - Lady
Door 1 - Tiger
Door 2 - Lady.
Since, the true second statement is suggesting there is lady behind 1 & tiger behind the other door, the possibilities of both tigers or ladies are eliminated.
That's why behind Door 1 is tiger & behind Door 2 is lady.
What three digits are represented by X, Y, and Z in this addition problem?
XZY
+XYZ
______
YZX
Here is the solution!
What was the problem?
Here is the equation rewritten.
XZY
+XYZ
______
YZX
Let's start with the tens place. Z + Y = Z is there. That means either Y = 0 or 9 if 1 is carry from ones place.
Since Y is at hundred's place it can't be 0. Hence, Y = 9.
At hundred's column, now we have, X + X = 9. That's only possible if X = 4 and carry 1 forwarded from tens place. So X = 4.
Now, finally, at ones place, we have, 9 + Z = 4. Hence, Z must be 5 with carry 1 being forwarded to the next place.
To sum up, X = 4, Y = 9 and Z = 5.
On a train, Smith, Robinson, and Jones are the fireman, the brakeman,
and the engineer (not necessarily respectively). Also aboard the train
are three passengers with the same names, Mr. Smith, Mr. Robinson, and
Mr. Jones.
(1) Mr. Robinson is a passenger. He lives in Detroit.
(2) The brakeman lives exactly halfway between Chicago and Detroit.
(3) Mr. Jones is a passenger. He earns exactly $20,000 per year.
(4) The brakeman’s nearest neighbor, one of the passengers, earns exactly three times as much as the brakeman.
(5) Smith is not a passenger. He beats the fireman in billiards.
(6) The passenger whose name is the same as the brakeman’s lives in Chicago.
Who is the engineer?
Want to know who? Click Here!
Would you like to read question first?
Let's list all the clues once again here.
(1) Mr. Robinson is a passenger. He lives in Detroit.
(2) The brakeman lives exactly halfway between Chicago and Detroit.
(3) Mr. Jones is a passenger. He earns exactly $20,000 per year.
(4) The brakeman’s nearest neighbor, one of the passengers, earns exactly three times as much as the brakeman.
(5) Smith is not a passenger. He beats the fireman in billiards.
(6) The passenger whose name is the same as the brakeman’s lives in Chicago.
Since as per (2), the brakeman lives exactly halfway between Chicago and Detroit, locations Chicago or Detroit can't be nearest to him. Hence, the passenger that (4) is suggesting must be nearer to brakeman than Chicago and Detroit.
Now as per (1), Mr. Robinson lives in Detroit, means he is not the nearest to brakeman. Mr.Jones earning is $20,000/year as per (3), which is not evenly divisible by 3. Hence, the passenger (4) is pointing is not Mr.Jones.
So neither Mr. Robinson not Mr.Jones but Mr.Smith is the nearest neighbor.
Now Mr. Robinson lives in Detroit and Mr.Smith is living in between Chicago and Detroit but nearer to brakeman. Hence, Mr. Jones must be living in Chicago.
According to (6), Jones must be name of the brakeman as he is sharing his name with the man living in Chicago.
And if Smith is not fireman as per (5), he must be an engineer!
