Math Riddles

 
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Question: Five pirates are parting ways after finding a treasure of 100 pieces of gold. The pirates decide to split it based on a vote. Each pirate, from oldest to youngest, gets to propose a plan on how to split the gold.

If at least 50 percent of the other remaining pirates agree on the plan, that is how they will split the gold. If less than 50 percent of the pirates agree, the pirate who came up with the plan will be thrown overboard. Each pirate is smart, greedy, and wants to throw as many others overboard as possible without reducing the amount of gold they get.

What plan can the first (oldest) pirate propose to live and get as much gold as possible?

Answer: He can propose a plan that he gets 98 pieces of gold, the 3rd pirate gets 1 piece, and the 5th pirate gets 1 as well.

If there were just 2 pirates the younger pirate would definitely deny the plan so he could get all of the gold.

If there were 3 pirates the first pirate can offer the second pirate 1 piece of gold and take the rest himself because the second pirate wouldn't get anything if he has to propose a plan himself.

If there were 4 pirates the first pirate could take 99 for himself and offer 1 to the youngest pirate. They would both agree. If the youngest disagrees then he won't get any gold in the next plan.

So when there are 5 pirates it is in the interest of the 3rd and 5th pirate to accept 1 piece, because if they don't they won't get anything in the next plan.

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Question: You have two books. One of them is upside-down and the other is rotated so the top of the book is facing you.

What is the sum of the first page in each book?

Answer: 2. The first page in each book is page number 1 regardless of how they are oriented and 1 + 1 = 2.

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Question: You have a flashlight that takes 2 working batteries. You have 8 batteries but only 4 of them work.

What is the fewest number of pairs you need to test to guarantee you can get the flashlight on?

Answer: 7. If you break the batteries into 3 groups: Two groups of 3 and one group of 2. By doing this you guarantee that one of the groups has 2 working batteries. Both of the groups of 3 have 3 possible combinations of 2 batteries and the group of 2 only has 1 combination. So, 3 + 3 + 1 = 7 tries at most to find two working batteries.

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Question: There are 100 passengers boarding a 100 passenger airplane. When passenger 1 gets onto the plane, he is dissoriented, so he randomly picks a seat. Each of the remaining passengers (2, 3, 4, etc.) get onto the plane and take their seat if it is available or picks one of the remaining seats at random if it is not.

What is the chance that the last passenger (passenger 100) will get his seat?

Answer: There is a 50 percent chance.

When the last passenger gets on seats 2 - 99 will be taken for sure. Each of these passengers would take their seats if they were available, so the only seat remaining at the end would be 1 or 100. So there is a 50 percent chance that passenger 100 would get seat 100.

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Question: If you have 30 white socks, 22 black socks, and 14 blue socks scattered across the floor in the dark, how many would you have to grab to get a matching pair?

Answer: 4. Once you grab 4 you will definitely have 2 of the same color.

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