Showing posts with label play jigsaw puzzles. Show all posts

Wednesday, August 26, 2015

A Special Old Guy

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mathematical nerd riddle
Alvin and Buzz are nerds and like doing nerdy things. So Alvin called Buzz one day...

"Buzz, I've finished tracing my family tree back from the year 500 AD, and I found one quite special guy".

"What's so special about him?" asked Buzz.

"Well, he was x years old in the year x^2 (x squared) and he had a son who was y years old in the year y^3 (y cubed)".

Buzz looked perplexed "Sorry Alvin, but I can't solve for x or y".

"Well, he was your age when his son was born." said Alvin.

"You're right" said Buzz "He was a special old guy! But I still can't solve for x or y".

How old was the old guy when his son was born?

 

Notes:
Assume that the nerds have the conversation this year, ie 2004 AD. 

A Special Old Guy Puzzle Solution

Firstly, we can say that the date of birth (DOB) for the special old guy (SOG) is:
Equation {a}:
DOB(SOG) = x^2 – x

Similarly, for the son of the special old guy (or SOSOG for short):

Equation {b}:
DOB(SOSOG) = y^3 – y

SOG's age when SOSOG was born was:
Equation {c}:
Age(SOG) = DOB(SOSOG) – DOB(SOG) = (y^3 – y) – (x^2 – x)

There are unlimited solutions to equation {c} so we need some assumptions and limits.

We know that SOG must have been between, say 10 years old and 100 years old when SOSOG was born:

Equation {d}:
10 < Age(SOG) < 100

We also know that both SOG and SOSOG were born some time since the year 500 AD:
Equation {e}:
500 < DOB(SOSOG) < 2004.

Based on equation {b} and {e} we can clearly see that there are only 5 solutions for y. They are y = 8, 9, 10, 11 or 12. Any other solutions for y are in breach of equation {e}.
For each of these possible solutions for y there is only a limited number of solutions for x that comply with {d}. They are:
 x     y
--------
21     8
22     8
26     9
27     9
31    10
36    11
41    12

Any other solutions for x and y are in breach of equation {d}.
SOG's age when his son was born can be calculated for each of these possible solutions by using equation {c} as follows:
 x      y     Age(SOG)
----------------------
21      8           84
22      8           42
26      9           70
27      9           18
31     10           60
36     11           60
41     12           76

So there are 7 different solutions, which is why Buzz said he couldn't solve for x and y.
Now comes the lateral part of the puzzle: Alvin informs Buzz that "...he was your age when his son was born". Of course, Buzz knows his own age. He should therefore be able to pick the correct solution from the list of 7 possible solutions shown above. However, he can't. That means that Buzz (and the special old guy) must be 60 because there are multiple solutions for an age of 60, whereas any other age would yield a unique solution. Any other age and Buzz would be able to solve.
A 60 year old father – quite a special old guy.

Sunday, August 16, 2015

Boxes, Beads, and a Blindfold

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You have been named as a traitor by the King, the punishment for this crime is death. Although he is a cruel tyrant he gives you one last chance at freedom. When you are finally brought before him he has this to say to you:

"There are 100 beads, 50 black and 50 white. You will be allowed to draw one bead, whilst blindfolded of course. If it is black you will be condemned to death, if it is white you will be set free".

angry king

So far so good you think to yourself, at least I have a 50/50 chance.

"The beads will be distributed amongst four boxes by me," he continued. "You must select a box by opening it, draw one bead from it and then present the bead to the court. Thus will your fate be decided".

Upon saying this a cruel smile appears on the King's face and you suddenly break into a cold sweat as you remember that the King is both very wicked and devilishly cunning.

Assuming that the King is incredibly smart, evil, thinks that you are a stupid, uneducated peasant and wants to minimise your chance of freedom, what strategy should you employ, and what is the probability of surviving?

 

Notes:
  • The King whilst evil won't cheat.
  • The trick is to work out how he plans on distributing the beads to minimise your chance of success.
  • As soon as you stick your hand in one of the boxes you must draw a bead from it.
  • The boxes and beads light and portable, however you are not allowed to remove them from the area.
  • The King thinks you are stupid.

Boxes, Beads, and a Blindfold Puzzle Solution

The king puts 1 black bead in 3 of the 4 boxes and all the other beads (both black and white) in the fourth box.

In the kings' view, you will just randomly pick a box because you are so stupid. This gives you barely 1 chance out of 8 to pick a white bead (1/4 to pick that one box containing white beads multiplied with almost 1/2 to pick a white bead out that box).

Assuming each of the four boxes are identical, by picking up each box in turn, you will be able to tell by weight or the rattling noises which one of the boxes contains the mixed beads. Picking the box with the mixed beads will mean that you have a slightly better than 50% chance of living.

Thanks to "Ben Leil" and "Kobold" for posting solutions in the forum

Friday, October 31, 2014

Scariest Halloween Pumpkins

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Just take a look at these terrible and funny at the same time the creations of artist John Neil. The technique of carving the pumpkin is amazing, as well as the artistic vision that reflects the whole spirit of this beautiful holiday - Halloween.










Friday, January 17, 2014

Stave Puzzles

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Stave Puzzles is an American jigsaw puzzle company located in Norwich, Vermont. The company was created in 1969 by Steve Richardson and Dave Tibbetts. They manufacture hand cut jigsaw puzzles made from cherry-backed, 5-layered, 1⁄4-inch (6.4 mm) wood. Stave produces several different types of puzzles ranging from traditional puzzles, teaser puzzles, trick puzzles and lately three dimensional puzzles, limited edition puzzles and complete custom puzzles.

Owners of Stave Puzzles include Queen Elizabeth II, Barbara Bush, Stephen King, Julie Andrews, Tom Peters, and Bill Gates.

The Stave Company of America make and sell the most expensive range of modern jigsaws. As long ago as 1993 a Stave puzzle was sold for over $12,000.  Stave make many jigsaws each year that are eagerly snapped up at prices of over $5,000 each.

Here are some examples of these amazing Jigsaw Puzzles.








Sunday, December 29, 2013

Benefits of Jigsaw Puzzles for Children

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There are several benefits any child can avail of by playing jigsaw puzzles, in boxes or online games. There are 3  ways in which jigsaw puzzle can prove beneficial for children’s proper growth & development:
  • Improves Hand – eye coordination: While playing jigsaw puzzles children learn how to observe the pieces and put them in the correct position. 
  • Enhances Brain & Memory Power: Jigsaw puzzles are very beneficial in developing a child’s mental and logical behavior in their early stages. It is also helpful in developing manual dexterity. As children get older, he/she will be able to proceed to more intricate puzzle games. This will further help develop and improve their other skills such as vernacular and numerals. 
  • Boosts morale: The successful completion of jigsaw puzzles presume a gratifying feeling in children. This in turn boosts a child’s morale and eventually children are motivated to play and finish more puzzles. Thus, they are also encouraged to move onto more complex puzzles. 
Puzzles Benefits

Friday, December 20, 2013

Puzzle Mansion

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The Puzzle Mansion holds the Guinness World Record title for having the largest jigsaw puzzle collection assembled by a single person
Jigsaw Puzzles

The main attraction here is the jigsaw puzzle museum of Ms. Gina Gil - Lacuna.  Her collection consists of 1,029 puzzles (but Guinness only considered 1,028) -- beating Brazil's record by a mile -- with a total of 700,004 puzzle pieces that she has done for 27 years.
JIgsaw Puzzles

Mona Lisa Puzzle

Friday, September 13, 2013

Interesting Facts on Puzzles History

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  • “Legpuzzel” is the dutch name for jigsaw puzzles and tangram-like puzzles.
  • Puzzel represents the most general word, encompassing logical puzzles, crosswords, mechanical puzzles and in general all kind of “problems” to solve.
  • On 18 october 1817 in Paris a booklet with the title “Le Casse-tĂȘte Chinois” was published and it was a copy of the English publication ” The Chinese Puzzle”.
  • In italy the etimology of word puzzles weas reflected in Rompicapo- Al Gioco Cinese chiamato il Rompi-Capo” was the title of an 1818 Italian publication.
  • The Spanish Rompecabezas is from some later date, probably introduced as Rompe-Cabezas as one of the titles of French export puzzles.
  • The German name Kopfzerbrecher has been used in 1891 as the name for the Anker tangram puzzle
  • “Chinese puzzles” became in the middle of nineteenth century the name for mechanical puzzles from Asia  - they were made in Japan or India.
  • Unlike word or jigsaw puzzles, mechanical puzzles are hand-held objects that must be manipulated to achieve a specific goal. These puzzles are often referred to as mechanical puzzles, brain teasers, 3D puzzles, mind benders, one person games, or just plain wooden games or wooden toys.