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?
ABC
DEF
GHJ

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.