The first solution was sent in by Jacob Graham. He made four rectangles.

The second solution was submitted by Andrei Laznau, School 205 Bucharest, who was able to make five rectangles but one of them contains only two numbers.

Can anyone improve on five or offer a different solution with 5 rectangles?

Is it possible to to distribute the numbers so there are no rectangles totalling 34, or just one, two or three?

Jacob's solution:

5 13 17
15 1 3
9 11
7 19

5 13 17
15 1 3
9 11
7 19

5 13 17
15 1 3
9 11
7 19

5 13 17
15 1 3
9 11
7 19


Andrei's solution:
First, I put number 19 in the top left-hand corner, because it is the biggest. I see that adding 15 to 19 gives 34, the number I should obtain. So, I place 15 in the opposite corner, in the top right.

19 15

Now, I see that

19 + 11 + 1 + 3 = 34

I place the numbers as follows:

19 15
1
3
11

I see that

34 - (19 + 1) = 14

and

14 = 9 + 5

I place the numbers in the big rectangle:

19 15
1 9 5
3
11

Now, I apply the same method, seeing that

11 + 3 = 9 + 5

and

34 - (13 + 7) = 11 + 3

19 15
1 9 5
3
11 13 7

19 15
1 9 5
3
11 13 7



I did not use 17, so I put it in the corner that was left:

19 15
1 9 5
3
11 13 7 17

In total I found five rectangles.