A packing company supplies storage boxes in three diﬀerent sizes: small, medium, and large. All three types of box have the same ratio of width:length and height:length. It is noted that: A. Eight small boxes ﬁt neatly inside one medium box. B. The length of the small box is the same as the height of the medium box. C. The base area (i.e. width times length) of a large box is 9 times smaller than the base area of the small box. D. The lengths of all three boxes added together is 2.4 m. E. The width of the medium box is twice the height of the small box. What are the lengths of the three diﬀerent boxes? What are the ratios of the width:height and width:length of the boxes?
Freight transport on Titan is mostly by ship, with three types of ship called pangs, quizzers, and roodles in common use. All three ships have the same shape and design but diﬀer in size. The cargo capacity depends on the hold volume, while the number of crew required is proportional to the surface area of the deck. A quizzer and a roodle taken together have the same length as two pangs, and the crew of a quizzer is just suﬃcient to provide crew for two pangs and a roodle. A fully loaded quizzer wishes to transfer all its cargo to smaller pangs and roodles, while minimising the number of crew required for the resultant ﬂeet. How many pangs and roodles are needed? [Hint: Note that for objects of any shape the surface area is proportional to the square of the object’s size, and the volume is proportional to the cube of its size.]
A forest is inhabited by three species of macaw which are all the same shape but are di®erent sizes and colours. The food consumption of each type is proportional to the square of its length. Given that (a) A crimson macaw and a ruby macaw put together are twice as long as a scarlet macaw (b) A crimson macaw and a scarlet macaw put together eat as much as a ruby macaw (c) 2 crimson macaws and a scarlet macaw put together are 1 m long determine the lengths of the three types of macaw.
I like these puzzles, and I want to practice them to get better at them (as I will be tested on similar puzzles), however, I can't seem to find any similar puzzles. These are the criteria:
Preferably, it has the same form as the above ones, where a couple of different objects have different properties, and you have to puzzle to find a certain asked property.
No advanced mathematics required, like in the puzzles.
That's basically it. These types of puzzles remind me of this famous puzzle, which was supposedly created by Einstein.