Spoiler Alert! Answers to problems

You may have seen three math problems in the Cheetah Chatter or in a kid-mail flyer.  They are challenging!  But they can be solved easily if you look at them the right way. 

These are the kinds of problems we learn to solve in math club.  If you enjoyed this challenge, come join us!

Did you try your best to solve them all?  Ready for the answers?  Read on.

1. Add all the counting numbers from 1 to 20. What do you get?

You might think of adding 1, 2, 3, etc. in order, all the way up to 20.  But there’s a faster way.

First write the numbers in a different order:

1+20 + 2+19 + 3+18 + 4+17 + 5+16 + 6+15 + 7+14 + 8+13 + 9+12 + 10+11

Now we can see that there are 10 pairs of numbers, and each pair adds up to 21.

10 x 21 = 210.


2. A says B lies. B says C lies. C says A and B both lie. Who is telling the truth?

“A says B lies”; therefore, A and B are opposites.  If B is a liar, then A is a truth-teller; but if B is a truth-teller, than A is a liar.

“C says A and B both lie”; but C is wrong.  C is saying that A and B are the same, but we just decided that A and B are opposites.  Therefore C is a liar.

“B says C lies”; therefore B and C are opposites.  Since C is a liar, B is telling the truth.

Advanced note:  You actually don’t need to know what C says in order to solve this problem.  “A says B lies” so A is the opposite of B.  “B says C lies” so B is the opposite of C.  Therefore A and C are the same, and B is their opposite.  The question asks who “is” telling the truth, which implies there is only one.  So A and C must be the liars, and B must be telling the truth.


3. How many different squares can be formed by connecting 4 of these 9 dots?  (Hints:  it’s not 4 or 5; tilt the page.)

image01

There are 6 different squares!  Here they are.

Blurbs

Hey, wait a minute….  Isn’t that 6th one a “diamond”?  Well, mathematically speaking, it counts as a square – because it has 4 equal sides and 4 right angles.


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