Throw out the 16 who don't visit any place. There are seven different combinations (all three (1x), two (3x), only one (3x)). 14 + 9 + 16 tourists have plans to visit the Gateway Arch plus some other place. In sum, 64 plan to visit the Gateway Arch, so 64 -14 -9 -16 = 25 visit the Gateway Arch and only the Gateway Arch. Same approach for the zoo yields 13 tourists who visit the zoo and only the zoo. For the seven different cominations, we now know the results for six of them. It has to add up to 100. That leaves those who visit the museum and only the museum: 100 - 14 - 11 -9 - 16 - 25 - 13 = 12. Or so I think.