A job opening for a Webmaster has three desirable skills: writing, design, and programming. Of the received applications, 30 have at least one of these skills: 18 know design, 20 can write well, and 23 have programming ability. There are 6 with writing and design skills only, 7 with just writing and programming, and 4 who can design and program but can't write. Only those with all three skills are interviewed. How many interviews are there?

The corect answer is 13.

The puzzle can be solved using venn diagram.

Draw 3 intersecting circles and name them as W (for writing), D (for designing) and P (for programming). The 3 intersecting circles will have 7 empty spaces. Name them as follows : a=W only, b=W & D, c=D only, d=D & P, e=P only, f=P & W, g= W, D & P. Thus, we have to find the value of g.

We get the following equations from the problem : b+d+f+g=30, b+c+d+g=18, a+b+f+g=20, d+e+f+g=23, b=6, f=7, d=4.

Substituting the values of b, f and d in the first equation, we get g=13 which is the answer.