An ICLR 2019 paper by Neklyudov, Egorov and Vetrov on an optimal choice of the proposal in an independent Metropolis algorithm I discovered via an X validated question. Namely whether or not the expected Metropolis-Hastings acceptance ratio is always one (which it is not when the support of the proposal is restricted). The paper mentions […]
Category: optimisation
Le Monde puzzle [#1099]
A simple 2×2 Le Monde mathematical puzzle: Arielle and Brandwein play a game out of two distinct even integers between 1500 and 2500, and y. Providing one another with either the pair (x/2,y+x/2) or the pair (x+y/2,y/2) until they run out of even possibilities or exceed 6 rounds. When x=2304, what is the value of […]
Le Monde puzzle [#1092]
A Latin square Le Monde mathematical puzzle that I found rather dreary: A hidden 3×3 board contains all numbers from 1 to 9. Anselm wants to guess the board and makes two proposals. Berenicke tells him how many entries are in the right rows and colums for each proposal, along with the information that no […]
Le Monde puzzle [#1088]
A board (Ising!) Le Monde mathematical puzzle in the optimisation mode, again: On a 7×7 board, what is the maximal number of locations that one can occupy when imposing at least two empty neighbours ? Which I tried to solve by brute force and simulated annealing (what else?!), first defining a target targ=function(tabz){ sum(tabz[-c(1,9),-c(1,9)]-1.2*(tabz[-c(1,9),-c(1,9)]*tabz[-c(8,9),-c(1,9)] +tabz[-c(1,9),-c(1,9)]*tabz[-c(1,2),-c(1,9)] […]
Le Monde puzzle [#1086]
A terse Le Monde mathematical puzzle in the optimisation mode: What is the maximal fraction of the surface of a triangle occupied by an inner triangle ABC where Abigail picks a summit A on a first side, Berenice B on a second side, and then Abigails picks C on the third side, towards Abigail maximising […]