On the TV channel SBS, in Australia, there is a TV show in which contestants have six numbers and the operations of addition, subtraction, multiplication and division with which to produce a three digit number.
My question is whether, for any 6 numbers, this is always possible, and if so, does it hold for any choice of 6 single digit numbers? What is the lower bound on how many numbers are required?
EDIT: The numbers must all be different. So (1,1,1,1,1,1) and (1,1,1,99,99,99) aren't allowed.
Best Answer
I assume the six numbers are all distinct, and each must be used exactly once. A brute-force program found, e.g. that with the six numbers 4, 6, 8, 16, 32, 64 the possible results did not include 571, 581, 587, 619, 623, 631, 649, 657, 661, 671, 673, 679, 681, 695, 709, 713, 721, 731, 743, 793, 811, 817, 821, 823, 827, 839, 841, 845, 849, 851, 853, 855, 857, 859, 863, 865, 871, 873, 877, 878, 879, 881, 887, 905, 911, 913, 917, 919, 921, 923, 933, 935, 937, 941, 943, 979, 983, 985, 987, 991, or 993.