A horrible puzzle! Find the four numbers which, using only the basic mathematical operators (addition, subtraction, multiplication and division) and each number once (or not at all), can make all the positive integers up to the highest possible value of n.
Explaining by example, if the question was to do this for only two numbers, the answer would be, unless I'm mistaken, 3 and 1, with n=4, thus:1 = 1 2 = 31 3 = 3 4 = 3+1 3 and 2 would be no good since, though it can make 5 (3+2) and 6 (3*2), it can't make 4, meaning its n stops at 3.
Answer in comments with any answers that beat the previous best answer. For a quick guess starting point to beat, take 1, 3, 9 and 18, which make for an n of 31. Alternatively, if you can't beat a previous answer, you could challenge it on an integer of n or less that you think it can't make. [01:36] [4 comments]

