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Bottle Football Player
Mindbender math puzzle...help?
There are 100 football players lined up from 100 to 1...Ahead of them are 100 water bottles lined up from 1 to 100. Football player #1 (in the front) goes and knocks all of the water bottles down and heads to the lockers. Football player #2 then adjusts all multiples of 2 in the group of bottles. Football player #3 adjusts all multiples of 3 in the group of bottles. This pattern continues for the rest of the football players. (Keep in mind that "adjusts" can mean set a water bottle up or knock it back over again, so a football player will never skip a bottle that is a multiple of his number.) The question is: How many bottles are left laying down after all 100 football players have adjusted them?
I'm trying to find a pattern to apply to this...possibly something to do with functions, prime numbers, or degrees? Any information that might help me find a solution are appreciated. Thanks.
It is to do with "Square" numbers 1, 4, 9,16, 25, 36, 49, 64, 81. 100.
All of these only have an odd number of factors eg 16's factors are 1, 2, 4, 8 and 16.
All other numbers always have an even number of factors. By definition a factor of a number is one that divides exactly into that number. Apart from squares therefore, one factor will always have a "partner" factor that makes up the number. Therefore all numbers have an even number of factors.
eg 20, factors are 1 and 20, 2 and 10, 4 and 5 = 6 factors = EVEN
Where there is a square it is odd eg the factors of 36 are 1 and 36, 2 and 18, 3 and 12, 4 and 9 and (6 and 6). Player 6 only turns the bottle ONCE so there are 9 turns = ODD
1 is a square number of 1 and gets left lying down (no other players can pick it up)
the 9th bottle is knocked over by player 1, picked up by player, 3 and knocked over by player 9 and is therefore left lying on the ground.
This will happen to all perfect square numbers - they will all be left lying on the ground.
All other numbers will be upright
eg 6 - knocked over by 1, picked up by 2, knocked over by 3, picked up by 6
18 - knocked over by 1, picked up by 2, knocked over by 3, picked up by 6, knocked over by 9, picked up by 18.
Therefore only the perfect squares will be left lying on the floor
Bottles 1, 4, 9, 16, 25, 36, 49, 64, 91 and 100. Total 10 bottles
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Do you know fair play ? Football match Japan vs China
Nike's Eco-Friendly Uniform For A Brazilian Team
Recently, Nike, one of the biggest apparel makers in the world announced that they will be sponsoring eco-friendly team uniforms for the Brazilian National Team. This is in cooperation with the Nike Middle East and Sun and Sand Sports. The uniforms come in what the makers called as kits which are composed of a set of sports uniforms. The kits given individually to Brazil's top football players will be worn on the event that will take place this summer in South Africa. One of the prominent recipient of this environmentally-friendly and technologically-advanced kit is Robinho (Robson de Souza) – the youngest player of the team.
"This summer in South Africa Nike will give footballers an edge by providing the newest and most innovative product for the game's greatest players," says Charlie Denson, President, Nike Brand in an interview. "With today's announcement, we are equipping athletes with newly designed uniforms that not only look great and deliver performance benefits, but are also made with recycled materials, creating less impact on our environment."
The rivalry in the fabric manufacturing industries does not end at making the highest qualities of products and on the most pioneering features but also on the mechanics in which the products affect the environment. This comes at a reality when major manufacturers of workwear uniforms and corporate uniforms for industrial and other work place utility chose to use eco-friendly fabric. This type of fabric is made purely of natural materials and has no effect to the environment from pre to post production. The process by which the fabric is made is as well can be considered as safe to the environment.
The beginning of the international clamor for environmental responsibility marks the start of this movement. This is also a response to the global claims of preventing the harmful climate change wherein natural calamities can occur at the most inconvenient of times and unexpected. Other industries like the automobile manufacturers and the petroleum companies have already set their feet off the usual and embraced the idea of saving the planet by creating cars that has lower carbon emissions and by generating fuel that contains lower carbon materials or using plants for bio-diesel correspondingly.
Since fabrics that are used in medical uniforms, corporate uniforms, hospitality apparels, jackets, and sports uniforms are created using elaborate machines that either use electricity or diesel, producers thought that it is but fitting that they shift to a more cost effective yet efficient process thus the eco-friendly fabrics. For the part of one of the highest producers of human needs, this movement is not just a good cause but as well as a brilliant idea.
The uniforms are actually made of recycled polyester with each, the jackets and the jerseys, were from 8 recycled plastic bottles. The unveiling of the kits was lead by the representative of the Embassy of Brasil, Mrs. Cecilia Bicca at the Mall of the Emirates. The report also read that all of the other Nike sponsored national teams that will vie this summer will be wearing the same athletic uniforms made of eco-friendly products – a first in Nike's history and the footballs history. The other national teams that will be using the said kits this summer event are the Netherlands, Portugal, USA, South Korea, Australia, New Zealand, Serbia, and Slovenia. Additionally, these great kits are also available commercially in selected outlets in the Middle East.
About the Author
Penelope Rock is a product consultant for online uniforms like corporate uniforms and other branded uniforms.
