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Puzzle
#98 



Pizza’s
pitfalls
You and a friend of yours wish to share a perfect circular pizza...
How would you split it into real EQUAL parts if you don’t know where the
center of the pizza is? (PS. You can use only a kitchen knife and a triangle
 setsquare, in UK  and you can't fold the pizza!)



Solution
A ('fair way' method)
To have subjective equal parts, one of you
cuts the slices, the other chooses...

Solution
B ('triangle' method)
This
method works only if the triangle is equal
or larger than the diameter of the pizza.
1. Put the right angle of the triangle on
perimeter of the pizza.
2. Then the two sides of the right angle
will meet the perimeter in two points A and
B. Mark these two points with the knife.
3. Using the triangle as a ruler, cut the
pizza in a straight line (the line that passes
through points A and B) and you'll get 2
equal parts.

Solution
C ('ABC' method)
1.
Mark a spot (A) on the edge of the pizza
by nicking the crust with the knife.
2. Using the length of the knife as a guide,
similarly mark two more spots (B and C) at
equal distances on each side of A.
3. Cut from B to C.
4. With the help of the triangle make another
cut starting from A, perpendicular to the
first cut and continuing to the other side
of the pizza. You have then 2 perfect equal
parts. That's all...

Solution
D
1. Pick an arbitrary point in the pizza
(O).
2. With the help of the triangle, cut the
pizza into 8 slices by cutting at 45 degree
angles through point O, and imagine that
alternate pieces are colored in brown and
green. Surprisingly, the area of all the
brown slices will always be equal the total
area of the green slices! So, to get equal
parts, each one of you have to pick up
slices of the same color... This theorem
can be proved by using calculus and polar
coordinates.
Question: if the number of slices
is 4, and the slices are cut at 90 degree
angles through an arbitrary point in the
pizza, does this theorem still work?

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Give
me the fruitful error any time,
full of seeds, bursting with its own corrections.
You can keep your sterile truth for yourself!
Vilfredo Pareto
The
Pareto Principle
(also
known as the '8020 Rule',
the 'law of the vital few' and
the 'principle of factor sparsity')
The
Pareto principle was suggested by management
thinker Joseph Juran.
It was named after Vilfredo
Pareto, a noted Italian economist
and sociologist, who made several important
contributions to economics, especially
in the study of income distribution and
in the analysis of individuals' choices.
The Pareto principle is a mathematical formulation which states that
the distribution of incomes and wealth in society is not random, but exhibits
a consistent pattern. This relationship follows a regular logarithmic pattern
and can be charted in a similar shape, regardless of the time period or country
studied.
The formula is: Log N = log A + m log x
where N is the
number of income earners who receive incomes
higher than x,
and A and m are
constants. In simplified terms, 80% of
the wealth is owned by 20% of the population.
In its generalized form, the principle
states that for many phenomena 80% of consequences
stem from 20% of the causes.
Hereafter
are a few examples where the Pareto principle
typically applies:
• 80 % of the traffic pollution is produced by 20 % of the vehicles,
• 80% of the traffic travels on 20% of the roads,
• 80 % of a stock is filled with 20 % of the products,
• 20 % of the customers account for 80 % of the sales volume,
• 80 % of the profit is achieved with 20 % of the customers,
• 80% of customer complaints are about the same 20% of projects, products
or services,
• 80% of your measurable results and progress will come from just 20% of
the items on your daily todo list,
• 80% of the clothes you wear are from 20% of your closet,
• 20% of Archimedes' Lab web pages are viewed by 80% of our visitors...
Sure, those figures are but rough approximations. They all emphasize
the highly nonlinear distribution of causes and effects or of means and objectives.
Employment of the Pareto principle improves everyday problemsolving
efficiency greatly. Rather than wasting time, energies and money on efforts to
correct everything, it is more profitable to focus the attention only on those
few variables, which are shown to account for most of the problem.

Suggest an
ORIGINAL Wunderkammer fact 





Everyone
has at least one logic or math puzzle that
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us yours and let all our readers enjoy them!


Puzzle
#11, logic, by Zigmund
Froid, D 
My
mother said: "I've placed 10 dollars
in your textbook between pages 125 and
126...", "Oh, thanks Mom!" I
answered, but most probably the bill will
be somewhere else. Why? 
Rate: •••• 
Solution
#11 

Puzzle
#12, maths, by Agon
K. Pech 
A
passenger fell asleep on the Heidi Express
panorama train halfway to his destination.
He slept till he had half as far to go
as he went while he slept. How much of
the whole trip panorama has he missed? 
Rate: •• 
Solution
#12 



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