puzzles

1

The circumference of the Earth is approximately 40,000 kilometres, and someone has just made a metal band that circles the Earth, touching the ground at all locations. You come along at night, as a practical joke, and add just 10 metres to its length (one hundredth of one kilometer !) It is now one four-millionth longer, and sits magically just above the ground at all locations How far has it risen ... could a flea, a rabbit or even a man squeeze underneath it? Did u get the answer? " " " " " " The Solution . . . Use the formula Circumference = 2 × pi × Radius Before: Original Circumference = 2 × pi × R After: Original Circumference + 10 = 2 × pi × (R + Gap) Subtracting the two: 10 = 2 × pi × Gap So, the Gap = 10 / (2 × pi) = 1.6m So a man could fit under it easily (though he might bump his head) 2 5 pirates of different ages have a treasure of 100 gold coins.  On their ship, they decide to split the coins using this scheme:  The oldest pirate proposes how to share the coins, and ALL pirates (including the oldest) vote for or against it.  If 50% or more of the pirates vote for it, then the coins will be shared that way. Otherwise, the pirate proposing the scheme will be thrown overboard, and the process is repeated with the pirates that remain. Assuming that all 5 pirates are intelligent, rational, greedy, and do not wish to die, (and are rather good at math for pirates) what will happen? Did u get the answer? " " " " " " Our Solution: The oldest pirate will propose a 98 : 0 : 1 : 0 : 1 split, in other words the oldest pirate gets 98 coins, the middle pirate gets 1 coin and the youngest gets 1 coin. Let us name the pirates (from oldest to youngest): A , B ,C , D and  E . Working backwards: 2 Pirates:  D splits the coins 100 : 0 (giving himself all the gold). His vote (50%) is enough to ensure the deal. 3 Pirates: C splits the coins 99 : 0 : 1. E will accept this deal (getting just 1 coin), because he knows that if he rejects the deal there will be only two pirates left, and he gets nothing. 4 Pirates: B splits the coins 99 : 0 : 0 : 1. By the same reasoning as before, E will support this deal. 5 Pirates: A splits the coins 98 : 0 : 1 : 0 : 1. By offering a gold coin to C (who would otherwise get nothing) he is assured of a deal.  3 How can I get the answer 24 by only using the numbers 8,8,3,3. You can use the main signs add, subtract multiply and divide. Did u get the answer? " " " " " " Our Solution:  8/(3-(8/3)) = 8/(1/3) = 24 4. What 5-digit number has the following features: If we put the numeral 1 at the beginning, we get a number three times smaller than if we put the numeral 1 at the end of the number. Did u get the answer? " " " " " " The Solution . . . Using an easy equation:  3(100000 + x) = 10x+1  (Why? Well, adding 100000 puts a 1 at the front of a five-digit number, and multiplying by 10 and adding 1 puts a 1 at the end of a number) Solving this gives: 10x+1 = 3(100000 + x)  10x+1 = 300000 + 3x  10x = 299999 + 3x 7x = 299999 x= 299999/7 = 42857 The answer is 42857. 5 When asked about his birthday, a man said: "The day before yesterday I was only 25 and next year I will turn 28." This is true only one day in a year - when was he born? Did u get the answer? " " " " " The Solution . . . He was born on December 31st and spoke about it on January 1st.