Count the Squares

March 13th, 2015

#1)

#3) The cheetah, one of the fastest mammals, has a top speed of 75 miles per hour.
The sloth, one of the slowest mammals, has a top speed of 13 feet per minute.
By what factor must the sloth's top speed be multiplied to equal the cheetah's
top speed? Express your answer to the nearest whole number.

Hints:
- be careful of UNITS
- What are asked to find?
- How should the answer look?

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#3) The cheetah, one of the fastest mammals, has a top speed of 75 miles per hour.
The sloth, one of the slowest mammals, has a top speed of 13 feet per minute.
By what factor must the sloth's top speed be multiplied to equal the cheetah's
top speed? Express your answer to the nearest whole number.

Hints:
- be careful of UNITS
- What are asked to find?
- How should the answer look?
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40th entry in column C

Octoberr

September 2014

Puzzles for September:

1) The sum of the FIRST FIVE PRIME NUMBERS
is DIVIDED by the FIRST PRIME NUMBER.
What is this Quotient?

2) When Bob's age is subtracted from Alice's age the 
answer is 20 less than the sum of their ages.
How old is Bob?

3) A jar is 1/4 full of marbles. If 25 marbles are
added to the jar, it becomes 1/3 full. How many
marbles does the jar hold when it is full?

4) You and I have some "ONE DOLLAR" Bills.
I have two more dollars than you. If I give you
one Bill, we will have the same number of bills. If you 
give me one bill, I will have twice as many as you.
How many dollars do you have?

5) A bookworm ate its way through 12 books lined on a shelf.
(It ate from outside the front binding - through all the pages -
to outside the back binding.) How far did it go if the front
of each book is 1/4 inch thick, the pages are 2 inches thick and 
the back binding is 1/4 inch in thickness?

6) Suppose that 
2 Hershey Kisses has the same fat content as 13 M&M's 
and 
3 Milk Duds have the same fat content as 15 M&M's.
Which of the following has the most fat content?

a) 3 Hershey Kisses and 1 Milk Dud
b) 25 M&M's
c) 4 Hershey Kisses
d) 1 Hershey Kiss and 4 Milk Duds

7) Suppose we define a NEW SYMBOL "#" through these examples:
5# means (5 times 4) or 20
4# means (4 times 3) or 12
With this in mind, evaluate the quotient
6#/3# 

8) On her birthday, Jill was 14 years old and her father Jack was 41.
Jill noticed that her age was the reverse of her father's age.
How old will Jill be the next time her age is again the reverse
of her father's age?

1)14       2)10       3)300      4)5


5)30         6)d        7)5         8)25

#9)

Click on the tiny picture below for the answer to #9. 

      

#10)

Click on the tiny picture

below for the answer to #10. 

The ANSWERS are

upsidedown!

#11) ARRANGE 10 COINS in a TRIANGULAR SHAPE.
Move just 3 coins to switch the way this Triangle points.
(From pointing UP to pointing DOWN!)

*

The

best way

to solve a puzzle

that uses objects is

to actually use these

objects.  In other words,

get out 10 pennies and put

them on a table to move around.

GOOD

LUCK!

Answer to #11) is BELOW - Click to see it!

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12)

Elmo bought a candy bar for FORTY CENTS.

He gave the cashier a DOLLAR.

How many different ways can the cashier make

change using only NICKELS, DIMES and QUARTERS?

  #12) 13 ways

13)
This is not a puzzle, but it gives an interesting result:

14)
Before you try #14 a quick review is in order:
%%%% SALE %%%% DISCOUNT %%%% SAVE %%%%
When we buy an item "ON SALE" and the store gives
us a discount, say 25% (25% OFF), there are two ways
to find the FINAL PRICE.

I) Multiply the Original (LIST) Price by .25
and then subtract this number (25% of the List Price)
from the LIST PRICE. (Thus, using two steps.)
II) A one step process of Multiply the ORIGINAL PRICE
by .75 and having this product be the Final Price.
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With the above explanation, try this puzzle:
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#14)  Which of the following two options
would save the most money?
Option #1: You can buy a $90.00 pair of shoes
with a single discount of 29%.
OR
Option #2: The same pair of shoes ($90) can have
SUCCESSIVE DISCOUNTS of 10% and then 20%.
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Try making you decision without performing
any arithmetic calculations.
After you make your choice, then actually
find the Final Prices under each Option.
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AFTER YOU HAVE ATTEMPTED THIS PUZZLE,
you can view the GENERAL solution by copying
the yellow region below.
*************SOLUTION***************
You were probably surprised to find that
the one 29% discount was the best!

A more Algebraic explanation follows:

Let the LIST PRICE be represented by N.
The first of two discounts,10% off,
can be found by taking the
LIST PRICE TIMES .9 -> .9(N)
Multiplying this .9(N) times .8 results in
(.8)(.9)(N) or (.72)(N)
This is equivalent to an 28% Discount.
*************SOLUTION***************

15)

#15) 8 was the input                  

summer problems 2014

summer problems

Click on the image for a LARGER VIEW!

http://www.pleacher.com/mp/probweek/p2002/a010702.html

#15

http://www.pleacher.com/mp/probweek/p2002/a010702.html


Try counting all the rectangles.
When you are finished, click on this link and see a picture
of a type of rectangle that you may have overlooked the first time.
Now go back and recount.
The most difficult thing in a problem like this is keeping
track (or labeling) of the ones that you counted.
By labeling each region you can list each rectangle as
a group of letters.
Click on this link to see a possible labeling and the
beginning of keeping track.
Now how many do you find?

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The Number Sequence Problem

What are the next three numbers in this sequence?
1, 8, 11, 18, 80, 81, 82, 83, 84, 85, 86, 87, 88, ...

Solution:
89, 100, 101.

The sequence consists of the positive integers (also called natural numbers) beginning with vowels.
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The Coin Problem

You have 64 coins, all of which appear identical. However, one of the coins is heavier than the others.
Using a two-pan balance, what is the least number of weighings that you need (in the worst case) to determine the false coin? Explain your process.

Solution:
You need only four weighings.

This proved to be a challenging problem. Most people sent in six for the solution because they divided the coins into two groups of 32.

To solve this in only four weighings,
Divide the coins into groups of 21, 21, and 22 coins.
Weigh the two groups of 21.
If one pan dips, then the false coin must be in that pan.
If the two pans balance, then the false coin must be in the group of 22.
Take the group with the heavier coin and split into 3 groups: 7, 7, and 8 (or 7).

Weigh two groups of 7. If they balance, the false coin is in the other group. If the pan dips, the false coin is in that group of coins.

Take the group of 7 (or 8) coins and split into three groups of 2, 2, and 3 (or 2, 3, and 3). Weigh the two equal groups of coins. If they balance, the false coin is in the other group. If the pan dips, the false coin is in that group.

You are now left with only 2 or 3 coins. Weigh two of them to determine the false coin.

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The Bellman Problem
Three people went to a hotel and rented a room for $30, each paying $10 for his share. Later, the clerk discovered that the price of the room was only $25. She handed the bellman five $1 bills and asked him to return them to the three people. The bellman, not knowing how to divide $5 among three people, instead gave each person $1 and kept the other $2 for himself.

Here's the question:
The three people originally paid $10 each, but each received $1 back, so they've now paid a total of $27 for the room.
Add to that the $2 that the bellman kept, and you have a total expenditure of $29 instead of $30. What happened to the other dollar?

Solution:
There is no missing dollar.
This is a classic problem -- it has been around for at least 30 years.


The total expenditure is now only $27, accounted for by adding the $25 in the hands of the hotel clerk to the $2 in the hands of the bellman.
In other words, the original $30 now is divided like this:
the hotel clerk has $25, the guests have $3, and the bellman has $2.

The error arose when an asset ($2) was added to an expense ($27) instead of the other asset ($25), thereby "mixing apples with oranges."


Solution:
A. 20    B. 6      C. 16      D. 10      E. 14
F. 18     G. 12     H. 22     I. 8    
The magic number was 42 -- Elvis' age at his death.

Jeopardy had this category on a COLLEGE TOURNAMENT in 2014

Jeopardy had this category on a COLLEGE TOURNAMENT in 2014

 Click on the image below
for the answers!