## Avernian posts

Posted in Mountains, pictures, Running, Travel with tags , , , , , , , , , , on August 31, 2014 by xi'an

## Boston sunrise

Posted in pictures, Travel with tags , , , , , , on August 7, 2014 by xi'an

## impressions, soleil couchant (#2)

Posted in pictures, Travel with tags , , , , , , , on July 12, 2014 by xi'an

## sunrise over Warwickshire (#2)

Posted in pictures, Running, Travel, University life with tags , , , , , on July 4, 2014 by xi'an

## back in Warwick

Posted in pictures, Running, Travel, University life with tags , , , on July 2, 2014 by xi'an

## sunset

Posted in pictures with tags , , , , , on June 21, 2014 by xi'an

## 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).