Archive for summer

Le Monde puzzle [#825]

Posted in Books, Kids, R with tags , , , , , on July 21, 2013 by xi'an

The current puzzle is the last one before the summer break and not exciting enough to take along:

Take the first ten digits, create five pairs out of those, and for each pair (x,y) derive the quantity (min(x,y)+1.5max(x,y)). What is the collection of pairs that maximises the product of those quantities?

I wrote the following R code in the train back from Annecy:

res=0
bonus=1.5
for (t in 1:1000){
x=matrix(sample(1:10),ncol=2)
mix=apply(x,1,min);mox=apply(x,1,max)
rex=prod(mix+bonus*mox)
if (rex>res){
  print(x)
  res=rex}
}

and got:

     [,1] [,2]
[1,]    4    7
[2,]    5    6
[3,]    8    3
[4,]    2    9
[5,]    1   10

Thus the sum of the pairs is always equal to 11. And by changing bonus you can check this is true for all values of the coefficient that are larger than one (one included).

new camera (stills)

Posted in pictures, Running with tags , , , , on June 15, 2013 by xi'an

IMG_0025IMG_0034

last caterpillar of the summer?

Posted in pictures with tags , , on October 14, 2012 by xi'an

 

bees in action

Posted in pictures with tags , , , , on October 7, 2012 by xi'an

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