# Brain Practice

May 2017

## Did you try the puzzles several times?

Here are the answers to Brain Practice, May 2017

**How Many Jewels?**

Tilly had 3 jewels – 1 ruby, 1 diamond and 1 emerald.

**How’s your Vocabulary?**

We found only three English words beginning with __dw__ :

**dwarf, dwell and dwindle**

Did you find any others?

#### **The Lucky Door Challenge.**

Probability problems are often among the hardest math concepts for students to wrap their heads around. Often, your common sense says one thing—but the answer is something else entirely!

- When you choose Door #1, your odds of winning are clearly 1/3.
- Therefore, the odds that the prize is behind Door #2 or Door #3 is 2/3.
- When Monty reveals that there is nothing behind Door #2, it doesn’t change the original probabilities.
*There is***still***a 2/3 chance that the prize is behind door two or three.*(Knowing the contents of door two doesn’t change the odds once you’ve started playing.) Therefore, door three now has a 2/3 odds of winning. - You should switch!

This is a very hard concept to absorb. Our intuition tells us that once Door #2 is eliminated, Door #1 and Door #3 each have a 1/2 probability of winning. But because the odds are set for good with your first pick, the winning odds of your original door will always stay at 1/3.

the writer of this puzzle said: * I worked with a NASA scientist who wouldn’t believe this answer. So we sat down and simulated the “game” a hundred times, where I was the host and he changed doors every time. Sure enough, he won about 2/3 of the games. If you need to be convinced, try it!*

**Three Equal Squares**

### 524127

This one was a real challenge! How did you go?

### 5 x (-2+4) x (1+2+7) = 100

**Who Gets what?**

John receives $24.50 and Bill receives 50 cents.

Using the ‘guess and check’ method, it goes like this:

- Try $24 and $1 – the first part is 24 times the second part. Not quite enough!
- Now halve the $1 to give two lots of 50 cents and add one lot to John’s $24.00.
- Now John’s part is $24.50 and Bill’s part is 50 cents.
- John has 49 times as much as Bill. Poor Bill He didn’t do very well out of that!

(Dividing a number by a half is the same as multiplying it by 2. that means that dividing $24.50 by 50 cents (half a dollar), we get the result 49.

Mathematicians, of course, will set up a pair of simultaneous equations and solve them that way!

## Need more practice?

Healthy Memory Workout is an eBook full of ‘how-to’s’ and puzzles to challenge your brain