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Jegadeesan
A banana plantation is located next to a desert. The plantation owner has 3000 bananas that he wants to transport to the market by camel, across a 1000 kilometer stretch of desert. The owner has only one camel, which carries a maximum of 1000 bananas at any moment in time, and eats one banana every kilometre it travels. What is the largest number of bananas that can be delivered at the market?
Answer:
750 bananas !!!
First of all travel 500 km (3 times)
first take 1000 bananas and put in half way and return again take 1000 banana drop in half way return and again take 1000 banana and drop it half way, i.e., at 500 km distance.
so now you have 1500 banana left at half distance.
Now take 1000 bananas and travel 250 km, drop it there and return and take 500 remaining bananas and travel 250 km and drop it. so now you have 1000 bananas left and a distance of 250 km is remaining. so take 1000 bananas and go. So at last you left with 750 bananas.
It's always 1 to 6, it's always 15 to 20, it's always 5, but it's never 21, unless it's flying. What is this?
Answer:
The answer is: a dice. An explanation: "It's always 1 to 6": the numbers on the faces of the dice, "it's always 15 to 20": the sum of the exposed faces when the dice comes to rest after being thrown, "it's always 5": the number of exposed faces when the dice is at rest, "but it's never 21": the sum of the exposed faces is never 21 when the dice is at rest, "unless it's flying": the sum of all exposed faces when the dice is flying is 21 (1 + 2 + 3 + 4 + 5 + 6)
A traveler, on his way to Eindhoven, reaches a road junction, where he can turn left or right. He knows that only one of the two roads leads to Eindhoven, but unfortunately, he does not know which one. Fortunately, he sees two twin-brothers standing at the road junction, and he decides to ask them for directions. The traveler knows that one of the two brothers always tells the truth and the other one always lies. Unfortunately, he does not know which one always tells the truth and which one always lies. How can the traveler find out the way to Eindhoven by asking just one question to one of the two brothers?
The question that the traveler should ask is: "Does the left road lead to Eindhoven according to your brother?" If the answer is "Yes", the traveler should turn right, and if the answer is "No", the traveler should turn left. Explanation: There are four possible cases: The traveler asks the question to the truth-telling brother, and the left road leads to Eindhoven. The truth-telling brother knows that his lying brother would say that the left road does not lead to Eindhoven, and so he answers "No". The traveler asks the question to the truth-telling brother, and the right road leads to Eindhoven. The truth-telling brother knows that his lying brother would say that the left road leads to Eindhoven, and so he answers "Yes". The traveler asks the question to the lying brother, and the left road leads to Eindhoven. The lying brother knows that his truth-telling brother would say that the left road leads to Eindhoven, and so he lies "No". The traveler asks the question to the lying brother, and the right road leads to Eindhoven. The lying brother knows that his truth-telling brother would say that the left road does not lead to Eindhoven, and so he lies "Yes"..
Barbara has boxes in three sizes: large, standard, and small. She puts 11 large boxes on a table. She leaves some of these boxes empty, and in all the other boxes she puts 8 standard boxes. She leaves some of these standard boxes empty, and in all the other standard boxes she puts 8 (empty) small boxes. Now, 102 of all the boxes on the table are empty. How many boxes has Barbara used in total?
It's a tough one.
Barbara uses 11 big boxed. that's for sure. Out of this, x big boxes are empty and 11-x boxes are filled - each with 8 medium boxes.
It comes to be that Barbara uses total of (11-x)*8 medium boxes. out of this y medium boxes are empty and (11-x)*8-y medium boxes contain small boxes - each contains 8 small boxes.
It comes to be that Barbara uses [(11-x)*8-y]*8 small boxes and it's GIVEN that all the small boxes are empty.
Now build the equation of the empty boxes:
x + y + [(11-x)*8-y]*8 = 102
Arranging the equation yields:
9x + y = 86
We know that x is between 1 and 10 (including) and y is between 1 and 79 (including) (it's given that there is at least one big and one medium empty boxes).
Now denote total amounts of big, medium and small boxes:
TB = 11
TM = (11-x)*8
TS = [(11-x)*8-y]*8
And try to put the numbers in the equation:
x=1 y=77 TS=24
x=2 y=68 TS=32
... ... ...
Finally calculate and add up the totals:
11 + 80 + 24 = 115
11 + 72 + 32 = 115
... ... ... = 115
As you can see, there might be various combinations of big, medium and small boxes that lead to the correct answer BUT there is only one correct answer.
Answer:
750 bananas !!!
First of all travel 500 km (3 times)
first take 1000 bananas and put in half way and return again take 1000 banana drop in half way return and again take 1000 banana and drop it half way, i.e., at 500 km distance.
so now you have 1500 banana left at half distance.
Now take 1000 bananas and travel 250 km, drop it there and return and take 500 remaining bananas and travel 250 km and drop it. so now you have 1000 bananas left and a distance of 250 km is remaining. so take 1000 bananas and go. So at last you left with 750 bananas.
It's always 1 to 6, it's always 15 to 20, it's always 5, but it's never 21, unless it's flying. What is this?
Answer:
The answer is: a dice. An explanation: "It's always 1 to 6": the numbers on the faces of the dice, "it's always 15 to 20": the sum of the exposed faces when the dice comes to rest after being thrown, "it's always 5": the number of exposed faces when the dice is at rest, "but it's never 21": the sum of the exposed faces is never 21 when the dice is at rest, "unless it's flying": the sum of all exposed faces when the dice is flying is 21 (1 + 2 + 3 + 4 + 5 + 6)
A traveler, on his way to Eindhoven, reaches a road junction, where he can turn left or right. He knows that only one of the two roads leads to Eindhoven, but unfortunately, he does not know which one. Fortunately, he sees two twin-brothers standing at the road junction, and he decides to ask them for directions. The traveler knows that one of the two brothers always tells the truth and the other one always lies. Unfortunately, he does not know which one always tells the truth and which one always lies. How can the traveler find out the way to Eindhoven by asking just one question to one of the two brothers?
The question that the traveler should ask is: "Does the left road lead to Eindhoven according to your brother?" If the answer is "Yes", the traveler should turn right, and if the answer is "No", the traveler should turn left. Explanation: There are four possible cases: The traveler asks the question to the truth-telling brother, and the left road leads to Eindhoven. The truth-telling brother knows that his lying brother would say that the left road does not lead to Eindhoven, and so he answers "No". The traveler asks the question to the truth-telling brother, and the right road leads to Eindhoven. The truth-telling brother knows that his lying brother would say that the left road leads to Eindhoven, and so he answers "Yes". The traveler asks the question to the lying brother, and the left road leads to Eindhoven. The lying brother knows that his truth-telling brother would say that the left road leads to Eindhoven, and so he lies "No". The traveler asks the question to the lying brother, and the right road leads to Eindhoven. The lying brother knows that his truth-telling brother would say that the left road does not lead to Eindhoven, and so he lies "Yes"..
Barbara has boxes in three sizes: large, standard, and small. She puts 11 large boxes on a table. She leaves some of these boxes empty, and in all the other boxes she puts 8 standard boxes. She leaves some of these standard boxes empty, and in all the other standard boxes she puts 8 (empty) small boxes. Now, 102 of all the boxes on the table are empty. How many boxes has Barbara used in total?
It's a tough one.
Barbara uses 11 big boxed. that's for sure. Out of this, x big boxes are empty and 11-x boxes are filled - each with 8 medium boxes.
It comes to be that Barbara uses total of (11-x)*8 medium boxes. out of this y medium boxes are empty and (11-x)*8-y medium boxes contain small boxes - each contains 8 small boxes.
It comes to be that Barbara uses [(11-x)*8-y]*8 small boxes and it's GIVEN that all the small boxes are empty.
Now build the equation of the empty boxes:
x + y + [(11-x)*8-y]*8 = 102
Arranging the equation yields:
9x + y = 86
We know that x is between 1 and 10 (including) and y is between 1 and 79 (including) (it's given that there is at least one big and one medium empty boxes).
Now denote total amounts of big, medium and small boxes:
TB = 11
TM = (11-x)*8
TS = [(11-x)*8-y]*8
And try to put the numbers in the equation:
x=1 y=77 TS=24
x=2 y=68 TS=32
... ... ...
Finally calculate and add up the totals:
11 + 80 + 24 = 115
11 + 72 + 32 = 115
... ... ... = 115
As you can see, there might be various combinations of big, medium and small boxes that lead to the correct answer BUT there is only one correct answer.
Posted in: Logical
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