13.  An anagram is a word or phrase whose letters can be rearranged to make some other word or phrase. For example: claim hat mate is an anagram of: mathematical. Here are 9 anagrams to be solved  each makes a single word which is used in mathematics  and ALL 9 must be done.  
laces  Vi died  crust in boat  
coster  Dina do it  cat liver  
use ream  Sam, cheat Tim  implicit in a lot 
14.  Starting in any cell of the grid on the right, moving up and down or across, but NOT diagonally, it is possible to make a tour which visits all 9 cells of the grid. A tour may start in any one of the 9 cells. Given that no cell may be visited more than once (so the tour cannot cross over itself) how many different tours are possible? 

15.  The drawing shows 2 oblongs with ABCD resting on top of AECF. Though the oblongs are of different sizes, corners A and C are coincident. All edges are an exact number of centimetres in length. What are the areas of the two smallest oblongs for which this is possible? 
The winner of Competition #4 was Henry Logan of Bromley
The answers were:
10.  Many possible answers 
11.  196 different squares 
12.  4.51% (to 3 sig. figs.) 