Prize Puzzle Competition 5

13.An anagram is a word or phrase whose letters can be re-arranged 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.
lacesVi died crust in boat
costerDina do it cat liver
use reamSam, 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.two oblongs 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.)
There was plenty of variety in the pandigital sums - only a few did some re-arranging of the '153' example.
Nearly everyone counted all the different squares correctly.
The error in the 'circle-squaring' method was found by many (and expressed in a variety of ways).
Well done.