Prize Puzzle Competition 14

. . . with a seasonal flavour . . .

Closing date is 31st December 1998

40. Here is a message for you.
In the array of letters on the right,
start at any letter and trace out the
message by moving from one square to
the next, moving up, down, across or
diagonally, using every letter in
order as you come to it, and using
no letter twice.
(Hint: all the letters are used)

What is the FULL message?

41. Christmas rhombus In the diagram on the left, you must start on the 'C' at one end and move to the 'S' at the other.
You must pass through 7 circles.
You can only move from one circle to another which touches it and must spell out the word 'CHRISTMAS' as you go.

How many different ways can this be done?

42. Father Christmas had a problem.
He was making up a batch of dolls but could not remember exactly how many of each kind he needed.
He knew that he needed 57 in total, that 27 had to have blue eyes, and 29 had to have fair hair.
His assistant gnome pointed out that some had to have both features and remembered that 3 dolls were needed having blue eyes and fair hair, but which were not able to say 'Mama'.
This prompted the old man to remember that he needed a total of 34 dolls able to say 'Mama', of whom 17 needed to have fair hair.
The assistant was going around in circles juggling all this information but couldn't work it out.
He pressed for any other bits of information that Father Christmas just might be able to manage, no matter how trivial.
The only items he got were: "every doll had at least 1 of the features named"; "that there was one combination of features not asked for at all" and "several children had asked for all 3 features in the one doll".
That was enough!

How many fair-haired, blue-eyed dolls saying 'Mama' were needed?

The winner of Competition #13 was Andrew Rackley of Our Lady and Saint John High School, Blackburn.
The answers were:

38.19p (1p for every straight line stroke)
39. 72 (2 by 2 by 2 and 4 by 4 by 4)
#37. If anyone did get this one wrong then it was not sent in.
#38. Not attempted by over half the entrants. Could it be because it did call for some lateral thinking?
A few mentioned the closeness of this one to Puzzle 19 in Comp#7, but at least no one tried giving the same answer.
#39. Though attempted by the majority of competitors, less than half of them got it right. Clearly those that got it wrong were either, merely guessing or, did not bother to see if their answer 'fitted' the problem.