Prize Puzzle Competition 12

Closing date is 28th August 1998

34. A group of boys and girls, all from the same family,
were brothers and sisters.
Each boy had as many sisters as he had brothers.
But each girl had only half as many sisters as she had brothers.
How many girls and how many boys were there?

35. Given the five digits 1, 2, 3, 4, 5 it is possible to make 120 different 5-digit numbers ranging from 12345 to 54321.
All (120) of these different numbers are made and added up.
What is the answer?

36. I have a rectangular picture whose edges are each an exact number of centimetres in length.
At a quick glance it could be mistaken for a square, but it isn't.
It is placed inside a black border which is 3 cm wide all the way around the picture.
By one of those coincidences (which always seem to happen in puzzles) the area of the border is exactly equal to the area of the picture.
picture + frame
What are the dimensions of the picture alone?

The winner of Competition #11 was Jennifer Lonn of Beaconsfield.
The answers were:

31.6 darts (4 x 17) + (2 x 16) = 100
32.6 by 8 by 12 = 576 cubic metres
33. Jill catches up with Jack after 30 minutes
In that time Rascal must have run 5 miles.
#31 All attempts entered were correct. Quite a few did not bother entering this one though.
#32 This one attracted the biggest entry in this competition and most of them were correct.
#33 Clearly the hardest of the three problems. Less than half those who attempted it got it right.