Leap Logic 3

In your sock drawer, you have a dozen socks: A half-dozen white socks, and a half-dozen red socks. You are about to pull out a pair of socks when the power goes out, plunging the entire room into darkness. What is the minimum number of socks you should take from the drawer to ensure you get a matching set of socks to wear?

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While house hunting in London, I came across a very good leasehold property Discussing the lease the landlady told me: "The property was originally on a 99 years lease and two-thirds of the time passed is equal to four-fifths of the time to come." How many years are to go?

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• 66

You are on a gameshow and the host shows you three doors. Behind one door is a suitcase with $1 million in it, and behind the other two doors are sacks of coal. The host tells you to choose a door, and that the prize behind that door will be yours to keep.

You point to one of the three doors. The host says, "Before we open the door you pointed to, I am going to open one of the other doors." He points to one of the other doors, and it swings open, revealing a sack of coal behind it.

"Now I will give you a choice," the host tells you. "You can either stick with the door you originally chose, or you can choose to switch to the other unopened door."

Should you switch doors, stick with your original choice, or does it not matter?

• Switch doors

• Stick with your original choice

• It doesn't matter

There is a large fresh water reservoir that has two distinct drainage systems - a small pipe and large pipe.

Six large pipes can drain the reservoir completely in exactly 12 hours while six small pipes will take 18 hours to drain the reservoir.

Can you calculate the time that will be taken by 6 large pipes and 6 small pipes together to drain the reservoir?

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• 6.0

• 7.2

• 8.4

• 11.6

Four friends need to cross a dangerous bridge at night. Unfortunately, they have only one torch and the bridge is too dangerous to cross without one. The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge. Times for each person: 1 min, 2 mins, 7 mins and 10 mins. What is the shortest time needed for all four of them to cross the bridge?

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Ten people land on a deserted island. There they find lots of coconuts and a monkey. During their first day they gather coconuts and put them all in a community pile. After working all day they decide to sleep and divide them into ten equal piles the next morning.

That night one castaway wakes up hungry and decides to take his share early. After dividing up the coconuts he finds he is one coconut short of ten equal piles. He also notices the monkey holding one more coconut. So he tries to take the monkey’s coconut to have a total evenly divisible by 10. However when he tries to take it the monkey conks him on the head with it and kills him.

Later another castaway wakes up hungry and decides to take his share early. On the way to the coconuts he finds the body of the first castaway, which pleases him because he will now be entitled to 1/9 of the total pile. After dividing them up into nine piles he is again one coconut short and tries to take the monkey’s slightly bloodied coconut. The monkey conks the second man on the head and kills him.

One by one each of the remaining castaways goes through the same process, until the 10th person to wake up gets the entire pile for himself. What is the smallest number of possible coconuts in the pile, not counting the monkeys?

• 511

• 1,009

• 2,519

• 5,039

• 3,628,799

What is the least number of people that need to be in a room such that there is greater than a 50% chance that at least two of the people have the same birthday?

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