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You are given a 52 digit number of the form
1111111...(25 times) [?] 1111.......(26 times)
Find the missing number '?' such that the resultant 52 digit number is divisible by 13.
Approach:
Lets assume 13 * X = 1111111...(25 times) [?] 1111.......(26 times)
The key to find the missing number is to find the X
What need should be the units place of X, it can be none another than 7 (7*13 = 91)
Now moving on to tens place of X, we again require a 1 at tens place at the output
so X has the tens place as 4, left as an exercise to the reader.
I similar fashion you can construct 13* 8547 = 00111111
Now we can create a sequence of 24 1's
13 * 008547008547008547008547 = 1111(24 times)
Now the problem reduces to finding a number such that
13 * Y = 1?11 (Since we 24 1's on the left and 24 1's on the right)
Y = 147 and ? = 9
Hence the missing number is 9
You having infinite number of planes and infinite supply of fuel in a airport station. Now each airplane has a fuel capacity to allow it to fly exactly 1/2 way around the world, along a circle.
The planes have the ability to refuel in flight. Though the fuel is unlimited, the island is the only source of fuel. What is the least number of aircraft necessary to get one plane all the way around the circle assuming that all of the aircraft must return safely to the airport?
Six pirates discover a chest containing 1 gold coin. They decide to sit down and devise a distribution strategy.
The pirates are ranked based on their experience (Pirate 1 to Pirate 6,
where Pirate 6 is the most experienced). The most experienced pirate gets to propose a plan and then all the pirates vote on it.
If at least half of the pirates agree on the plan, the gold is split according to the proposal. If not, the most experienced pirate is thrown off the ship and this process continues with the remaining pirates until a proposal is accepted. The first priority of the pirates is to stay alive and second to maximize the gold they get.
Pirate 6 devises a plan which he knows will keep him alive. What is his plan of the distribution of the gold coins?
Approach:
Lets start the bottom up approach.
Lets say there was only 1 Pirate. It is straightforward that the coin would be with him and he would be alive.
For the case of 2 Pirates, the 2nd pirate would keep the coin with himself as he himself holds a share of 50% votes, leaving him alive and with 1 coin.
For the case of 3 pirates, if the 3rd pirate keeps the coin with himself then 2nd pirate would surely vote against him, as on his death the problem reduces to the case of 2 pirates where he would get the coin. 1st pirate is unaffected by this as he is not getting any advantage, so he may or may not vote for the 3rd pirate.
So essentially with this distribution the 3rd pirate holds a chance to get voted out and die.
To avoid this, 3rd pirate need to lure the 1st pirate which would happen only if he give the distribution of 1, 0, 0.
Similarly moving ahead you could arrive on the correct answer. In case you do, plz post in the comments and the approach
Given a fleet of 50 trucks, each with a full fuel tank and a range of 100 miles, how far can you deliver a payload?
You can transfer the payload from truck to truck, and you can transfer fuel from truck to truck. Assume all the payload will fit in one truck.
If your answer is 5000 miles, its time to reread the problem :)
Approach:
Lets say after moving x miles, each of the truck is having the fuel of 100 - x miles left
In order to optimally utilize the fuel the fuel left in one tank should be equal to suffice the fuel consumed in other tanks.
So,
(100 - x)/49 = x
x = 100/50
So at the end of 2 miles each of the 49 trucks have the fuel capacity of 100 miles.
Can you similarly work it out now for the maximum distance covered.
