Prize Puzzle Competition 10

Closing date is 1st May 1998

28. A man is aged 71 and his daughter is 34.
(a) What age will the daughter be when she is
half the age of her father?
(b) What age was the man when he was
three times the age of his daughter?

29. Here is a magic square using the numbers 1 to 16 (with no repeats) arranged so the magic total of the numbers along every row, column and diagonal is 34.
It is possible, by replacing ONLY ONE of the numbers and then re-arranging all of them, to make the magic total 36.
To do that - which number must be replaced by what?
114 154
811 105
127 69
132 316

30. two triangles Both the sails of my boat are in the shape of a right-angled triangle.
They are of different areas, each being an exact number of square metres.
All their edge lengths are different as well, but each is an exact number of metres.
However, they do have one property in common. The area of each is numerically equal to its perimeter.
What is the area of each sail?

The winner of Competition #9 was Linda Phillips of Sutton Coldfield
The answers were:

25.35 triangles
26.Kit, Phil, Alexis, Terri
27. 50/(4 + pi) or 7.00 sq.metres (to 3 sig. figs.)
#25 was answered correctly by most entrants.
#26 was easy - everyone got it right!
#27 was not attempted by most candidates or, at least, not submitted. Nearly all of the answers received were correct.