Documents
Resources
Learning Center
Upload
Plans & pricing Sign in
Sign Out

puzzles - DOC

VIEWS: 145 PAGES: 13

									Squares vs Cubes
     From Asim Shah: Find the two smallest numbers whose difference between
     their squares is a cube and whose difference between their cubes is a square.
     As a hint and encouragement, both numbers are between 3 and 12. The next
     such pair is 384, 640.
4A = 6V
     George Sicherman has shown that 4A = 6V.




Red Green Blue Maze
     Chris Lusby Taylor: I've just been asked to do something for a local school's
     playground. I planned to use the existing paving slabs as squares but then
     found that they're laid in an offset pattern, so each has six neighbours.


     Enter at the top, cross the blue, green, and red bars, and keep this sequence
     until you exit at the bottom. Or enter at the bottom, and cross the red green
     and blue bars, and keep this sequence until you exist at the top.




A problem of squares
     Bernardo Recamán Santos: Find a four-digit square number which has at
     least one digit in common with every other four-digit square number.
 Toothpick Giraffe Puzzle. Five toothpicks form the giraffe shown above.
Change the position of just one pick and leave the giraffe in exactly the same
form as before. The re-formed animal may alter its orientation or be mirror
reversed but must have its pattern unchanged.




The Zen of Labyrinth
      Robert Abbott: Dave Phillips wrote a new maze book called "The Zen of the
      Labyrinth."                 I               reviewed                  it                here:


      http://www.logicmazes.com/reviews.html


      I thought one of his mazes would look great on mathpuzzle.com, so a GIF of
      the maze is the first attachment here. Dave says you have his permission to
      use           the          maze.           These           are             the          rules:


        Enter by the bottom red path and end on the center gray square.


        You   may     retrace    your    path    but   may     not   make        a   U-turn   on   a
        pathway.      You   must      follow     the   paths    in   the    order      red,   blue,
        yellow   and      then   red,    blue,    yellow   again,      as   needed,      changing
        color on the white squares.
NPR Puzzle
     The puzzle from NPR this week is mine. "This challenge comes with help from
     math puzzle expert Ed Pegg. Take the names of the first nine elements of the
     periodic table: hydrogen, helium, lithium, beryllium, boron, carbon, nitrogen,
     oxygen and fluorine. Select one letter from each of these names in order to
     spell a familiar nine-letter word. Hint: It's a word used in math." Send
     Answer.
     Here's a similar puzzle that Will Shortz though was slightly too obscure: Take
     the names of the officially recognized planets in order, Mercury, Venus,
     Earth, Mars, Jupiter, Saturn, Uranus, Neptune. Select one letter from each of
     these names in order to spell a familiar eight-letter name. Hint: It's a name
     used in math. Answer.
Erich Friedman Puzzles
     Erich Friedman: Multi-Balance Puzzles, Pyramid Puzzles, Crypto-Product
     Puzzles, Weight Equation Puzzles, Gold Star Puzzles, and Packing Puzzles
     have been added to Erich's Puzzle Palace. For example, for Weight Equations,
     put a digit in each box so that the equation is true. The boxes should also
     balance, where each digit represents the weight of that box. (His entry on
     Packing Problems at Math Magic this month is also very nice.)




Late Christmas Tree
     Serhiy Grabarchuk: Here is a Strimko inspired Christmas tree.
                            24 from 8,8,3,3
Puzzles -> Number Puzzles

How can I get the answer 24 by only using the numbers 8,8,3,3.
You can use the main signs add, subtract multiply and divide.

Answer
8/(3-(8/3))

= 8/(1/3)
= 24
                            5-digit Number


             What 5-digit number has the following features:

If we put the numeral 1 at the beginning, we get a number three times smaller than if we
put the numeral 1 at the end of the number?

Answer
Using an easy equation:

3(100000 + x) = 10x+1

(Why? Well, adding 100000 puts a 1 at the front of a five-digit number, and multiplying
by 10 and adding 1 puts a 1 at the end of a number)

Solving this gives:

10x+1 = 3(100000 + x)
10x+1 = 300000 + 3x
10x = 299999 + 3x
7x = 299999
x= 299999/7 = 42857

The answer is 42857.


                                   Birthday
Puzzles -> Number Puzzles




             When asked about his birthday, a man said:

"The day before yesterday I was only 25 and next year I will turn 28."
This is true only one day in a year - when was he born?
Answer:
He was born on December 31st and spoke about it on January 1st.




      Choose the Right Symbol - Solution
Puzzles -> Number Puzzles




              The Puzzle: What mathematical symbol can be put between 5 and 9, to
  get a number bigger than 5 and smaller than 9?


Answer
A Decimal Point

5.9 works nicely
  The Puzzle: A popular mathematical pastime:

  Use exactly four 4's to form every integer from 0 to 50, using only the operators +, -,
  x, /, () (brackets) x2 (square), and ! (factorial).

  Example: 0 = 44-44

Answer
0 = 44-44
1 = 44/44 or (4+4)/(4+4) or (4/4) / (4/4)
2 = 4/4+4/4
3 = (4+4+4)/4
4 = 4*(4-4)+4
5 = (4*4+4)/4
6 = 4*.4+4.4
7 = 44/4-4
8 = 4+4.4-.4
9 = 4/4+4+4
10 = 44/4.4
11 = 4/.4+4/4
12 = (44+4)/4
13 = 4!-44/4
14 = 4*(4-.4)-.4
15 = 44/4+4
16 = .4*(44-4)
17 = 4/4+4*4
18 = 44*.4+.4
19 = 4!-4-4/4
20 = 4*(4/4+4)
21 = (4.4+4)/.4
22 = 44*sqrt(4)/4
23 = (4*4!-4)/4
24 = 4*4+4+4
25 = (4*4!+4)/4
26 = 4/.4+4*4
27 = 4-4/4+4!
28 = 44-4*4
29 = 4/.4/.4+4
30 = (4+4+4)/.4
31 = (4!+4)/4+4!
32 = 4*4+4*4
33 = (4-.4)/.4+4!
34 = 44-4/.4
35 = 44/4+4!
36 = 44-4-4
37 = (sqrt(4)+4!)/sqrt(4)+4!
38 = 44-4!/4
39 = (4*4-.4)/.4
40 = 44-sqrt(4*4)
41 = (sqrt(4)+4!)/.4-4!
42 = sqrt(4)+44-4
43 = 44-4/4
44 = 44.4-.4
45 = 4/4+44
46 = 44-sqrt(4)+4
47 = 4!+4!-4/4
48 = 4*(4+4+4)
49 = (4!-4.4)/.4
50 = 4!/4+44
                        Fraction - Solution
Puzzles -> Number Puzzles




                The Puzzle: Can you arrange the numerals 1 to 9 (1, 2, 3, 4, 5, 6, 7, 8
  and 9) in a single fraction that equals exactly 1/3 (one third)?

  Example that doesn't work: 7192/38456 = 0.187


                                             .
                                             .
                                             .
                                             .
                             (Scroll down if you really want
                                 to see the Solution ...)
                                             .
                                             .
                                             .
                                             .
                                             .
                                             .

The Solution . . .
5832/17496 = 1/3
               Tricky Equation - Solution
Puzzles -> Number Puzzles




              The Puzzle: The following equation is wrong: 101 - 102 = 1

  Move one numeral to make it correct.

  (Caution: Trick)


                                            .
                                            .
                                            .
                                            .
                            (Scroll down if you really want
                                to see the Solution ...)
                                            .
                                            .
                                            .
                                            .
                                            .
                                            .

The Solution . . .
Move the numeral 2 half a line up to achieve 101-102 = 1
                       Cut Cube - Solution
Puzzles -> Logic Puzzles




                   The Puzzle: A solid, four-inch cube of wood is coated with blue
  paint on all six sides.

  Then the cube is cut into smaller one-inch cubes.

  These new one-inch cubes will have either three blue sides, two blue sides, one blue
  side, or no blue sides. How many of each will there be?


                                             .
                                             .
                                             .
                                             .
                             (Scroll down if you really want
                                 to see the Solution ...)
                                             .
                                             .
                                             .
                                             .
                                             .
                                             .

The Solution . . .
There are 24 with one side colored, 8 with three sides colored, 24 with two sides colored,
and 8 with no sides colored.
               Explain: Elevator - Solution
Puzzles -> Logic Puzzles




                 The Puzzle: A Man works on the 10th floor and always takes the
  elevator down to ground level at the end of the day.

  Yet every morning he only takes the elevator to the 7th floor and walks up the stairs
  to the 10th floor, even when is in a hurry.

  Why?


                                              .
                                              .
                                              .
                                              .
                              (Scroll down if you really want
                                  to see the Solution ...)
                                              .
                                              .
                                              .
                                              .
                                              .
                                              .

The Solution . . .
He is too short to reach the "10" button.


  The Puzzle: A man walks into a bar and asks the bartender for a glass of water.

  But the bartender takes out a gun and aims it at the man's head.

  The man says "Thank You" and walks out.

  Why?


                                             .
                                             .
                                             .
                                             .
                             (Scroll down if you really want
                                 to see the Solution ...)
                                             .
                                             .
                                             .
                                             .
                                             .
                                             .

The Solution . . .
The man had hiccups.

He wanted to cure it with a glass of water, but the bartender cured it by giving him a
surprise.

								
To top