If there are 10 pairs of cleats from brand A, 8 pairs of cleats from brand B, 6 pairs of cleats from brand C and 4 pairs of cleats from brand D, what is the minimum number of random selections to ensure a show for each foot (left or right) from the same brand?
I’m not sure about this but my thought process is thinking of worst case scenario where you pick 10 left (or right) cleats of brand A, then 8 left cleats of B, then 6 left cleats of C and 4 left cleats of D. The next one has to have a complete pair, this gives: 10+8+6+4+1=29
Is this correct or is there a faster way to guarantee pair?
The worst case scenario would be in-line with what you described. After getting 28 cleats of one side from all brands, you would have to pick up one of the other side. Therefore the least number of cleats one would have to pick up to ensure that there is at least one pair from at least one brand is 29, as you described.
PS : sorry for the previous blunder. Due to my ignorance, I didn't read the proposed problem properly at first. Thanks to Sten for pointing out my mistake.