22 Jul

DataGenetics – The Two Egg Problem

You are given two eggs, and access to a 100-storey building. Both eggs are identical. The aim is to find out the highest floor from which an egg will not break when dropped out of a window from that floor. If an egg is dropped and does not break, it is undamaged and can be dropped again. However, once an egg is broken, that’s it for that egg.

If an egg breaks when dropped from floor n, then it would also have broken from any floor above that. If an egg survives a fall, then it will survive any fall shorter than that.

The question is: What strategy should you adopt to minimize the number egg drops it takes to find the solution?. (And what is the worst case for the number of drops it will take?)

There are no tricks, gotchas or other devious ruses. Don’t rat-hole with issues related to terminal velocity, potential energy or wind resistance. This is a math puzzle plain and simple.

Think about the puzzle for a few minutes, and then read on.

via DataGenetics – The Two Egg Problem. Like brain-teasers and computer science algorthims, read on indeed.

13 Dec

BBC News – Cambridge University puts Isaac Newton papers online

The notebooks in which Sir Isaac Newton worked out the theories on which much classical science is based have been put online by Cambridge University.

More than 4,000 pages have been scanned, including his annotated copy of Principia Mathematica, containing Newton’s laws of motion and gravity.

Newton wrote mainly in Latin and Greek, the scientific language of his time, and was reluctant to publish.

The university plans to put almost all of its Newton collection online.

The papers mark the launch of the Cambridge Digital Library project to digitise its collections.

As well as Principia and Newton’s college notebooks, the Newton Papers section of the online library contains his “Waste Book”.

The large notebook was inherited from his stepfather, and scholars believe it helped Newton to make significant breakthroughs in the field of calculus.

via BBC News – Cambridge University puts Isaac Newton papers online. One of the geniuses of all time.

07 Jan

One isn’t Many and Many isn’t All

One of the arguments that I hear for why people express an -ism belief (racism, sexism, ageism, etc), is that they had this experience with this one person and you know that must be how everyone of that particular group is. I love this kind of reasoning it’s so illogical it’s almost funny and yet people do it all the time.

Venn Diagram: Subsets

Venn Diagram: Subsets

Mathematics will let you know that a subset is not always equal or the same as the larger set contained in it.

So why is that people assume that it is? Who knows, I suspect it has something to do with the same reason we are bad at assessing on an intuitive level risk.

Be that as it may, maybe it would be fair for people who make those sort of assumptions that a subset is the whole set to decide that white Americans are out to destroy America, or that Christians want to kill people and blow up buildings. Yet we don’t assume that because it just isn’t true.

So do you still think the one is the many and that many is all or is it possible that it just isn’t true?