# Prize Puzzle Competition 4

 10 A pandigital sum (for addition, subtraction, multiplication or division) is one which uses all of the digits 1 to 9 once and once only.For example -
 128 + 439 = 56726 + 48 + 79 = 153which are two pandigital addition sums,and there are many more like that. Find TWO other pandigital sums.

 11 How many distinct squares (not necessarily different in size) can be traced out following only the lines of the grid drawn on the right? 12 A very old problem is that of "squaring the circle". This means finding a way of constructing a square which is equal in area to a given circle.Many have attempted to solve this problem but were doomed to failure since it has been proved to be impossible.One method that was suggested was as follows -Draw the largest possible equilateral triangle inside the circle. Then draw a square which has one edge in common with the triangle and this square should have the same area as the circle.It is close, but it doesn't work!What is the difference in area between the square and the circle, expressed as a percentage of the area of the circle?

The winner of Competition #3 was Nick Lennard of Basingstoke
The answers were:

 7. Some of the possible solutions are - 12 + 3 + 4 + 5 - 6 - 7 + 89 1 + 23 - 4 + 56 + 7 + 8 + 9 1 + 2 + 34 - 5 + 67 - 8 + 9 1 + 2 + 3 - 4 + 5 + 6 + 78 + 9 123 + 45 - 67 + 8 - 9 123 - 45 - 67 + 89 8. Other answers might be possible, but the original message read - TINY LEAKS WILL SINK MIGHTY SHIPS 9. Area of lawn was 186.51 square metres (to 2 d.p.)
Fortunes were very mixed this time. All entries contained at least one correct solution to number 7 (and that was all that was required) with some giving as many ten. Nobody gave the solution which starts with -1.
There were NO correct solutions to number 8, but a couple were very close.
Roughly half the entries were correct for number 9.