# Prize Puzzle Competition 6

 16. A group of people were gathered together in one room and it was possible to count them using the following descriptions - 1 grandmother 1 brother 1 grandfather 2 sisters 2 fathers 2 sons 2 mothers 2 daughters 4 children 1 father-in-law 3 grandchildren 1 mother-in-law 1 daughter-in-law This gives a total of 23 people.But there were a lot less than that.What is the LEAST number of people that could have been present in the room?

 17 Use the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and use each digit once and once only.Divide the ten digits into two groups of five, and then arrange the digits in each group of five to make a multiplication sum.It could be done like this0, 1, 5, 6, 9 used to make 106 x 59 (which is 6254)2, 3, 4, 7, 8 used to make 437 x 82 (which is 35834)and the two multiplication sums have different answers.Find a way that makes the answers to both multiplication sums the same.

 18. The drawing (which is NOT to scale) shows the shape of a 1-hectare field. (It is a trapezium)The wider end is 60 metres long, and the narrower end is 40 metres long. The dotted line is a fence which divides the field into two parts which are equal in area.How far is the fence from the wide end? (To the nearest metre will do.)A hectare is 10000 square metres.

The winner of Competition #5 was Helen Galloway of Manchester
The answers were:

 13 scale, divided, subtractionsector, addition, verticalmeasure, mathematics, multiplication 14 40 15 8 and 28 (1 by 8 and 4 by 7)
The anagrams were completely solved in almost every entry.
Counting the tours did not produce a lot of correct entries.
Some large numbers indicated that entrants lost track of which cells they had already visited once.
A few thought "different" should have been defined. In this case, assuming a tour was recorded by the letters of the cells visited, "different" would be applied to the ordering that string of letters.
Not too many wrong answers among those who did attempt to find the sizes of the overlapping squares.