text: Let us assume that each photograph is rectangular. The photographs must have different length of sides, which are in the range 1 through 10. Also, the sides of the photographs must be such that the sum of the area of all of them equals 150 cm^2. Further, the sides should be such that these 5 photographs can be arranged in a 15 cm * 10 cm frame. If the dimensions of the n-th photograph be ‘an’ and ‘bn’ then\n\na1*b1 + a2*b2 + a3*b3 + a4*b4 + a5*b5 = 150 _________(1).\n\nBy trial we find\n10*1 + 9*8 + 7*6 + 5*4 + 3*2 = 10 + 72 + 42 + 20 + 6 = 150.\n\nWe also find that these dimensions can be arranged in a rectangle of dimensions 15*10 as shown in the fig. that you I have sent you by email.\n\nThe form 10*1 implies a rectangle which has its 10 unit long side parallel to the X-axis and 1 unit long side parallel to the Y-axis.\n\nHowever, not all the combinations satisfying equation (1) can be arranged in the aforesaid frame. Let us take the combination [1*8, 2*7, 3*6, 4*5, 9*10]. The sum of these 5 terms is 150 but these 5 rectangles cannot be arranged in a 15*10 frame.