Problems

Working out your mind is just like working out your body. You need to push yourself to build stamina and strength, it takes practice on new problems, and determination and grit to get there.

Here are some tough problems that allow you to do just that!

Samantha is 16 and thus twice as old as Allison was when Samantha was as old as Allison is today.  How old is Allison?

A ranger, a poacher a mother lion and her two cubs and a mother elephant and her two calves have to cross the Mara river in a raft.  The poacher can’t be left in the presence of any of the animals without the ranger present.  Further, the mother lion insists that her cubs can’t be in the presence of the mother elephant without her presence and the mother elephant demands that her calves not be in the presence of the mother lion without her there to protect them.  Only the mother lion, mother elephant and the ranger can pilot the raft, which can only hold two members of the party at a time.  What is the procedure that will result in everyone crossing safely?

The sum of the monkey’s age and her mother’s age is 4 years.  In addition, the monkey’s mother is twice as old as the monkey was when the monkey’s mother was half as old as the monkey will be when the monkey is three times as old as the monkey’s mother was when the monkey’s mother was three times as old as the monkey.  What are the ages of the monkeys?

Your friend is studying for his grueling physics final exam and is known to study 20% of the time at one of three libraries and 40% of the time at home. He did not bring his cellphone so you have no way of contacting him, but you have already checked two of the libraries. What is the probability that your friend is studying at home?

There is a power failure and you need a flashlight.  In a drawer, you have four dead batteries (which you like to keep for some reason), a pack of four new batteries and a flashlight that requires two batteries.  As you open the four-pack of new batteries in the dark, they spill into the drawer, so now you have a mixture of four good and four dead batteries and you can’t tell which is which.  You can test them only by placing two batteries into the flashlight and seeing if it works.   What battery checking protocol will minimize the number of tests needed to find two good batteries?

What is the minimum number of tests needed?

During World War II war, Russian cities near the front were blacked out.  In some cases, this meant that the citizens boarded up their windows.  Vanya has a 120″ by 120″ window in the front of his house that needs to be boarded up.  He has a 90″ by 160″ piece of plywood which happens to have the same area of the window.  Can you cut the plywood into TWO pieces such that they fit together to form a 120″ by 120″ square?  Show the cut in the space below.

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