Here is a Venn diagram which will cover the problem. It consists of 8 regions created by interlocking circles. Each circle represents a set of objects. Below is a reference key for the lettered regions. The letters represent the number of people taking the various flavours, including people that take none of them.
A Vanilla only
B Chocolate only
C Strawberry only
D Vanilla and strawberry but not chocolate
E Chocolate and strawberry but not vanilla
F Vanilla and chocolate but not strawberry
G All three flavours
H None
We can start assigning numbers:
A+B+C+D+E+F+G+H=100 (the regions added together make up 100 people)
A+D+F+G=56 (vanilla)
B+E+F+G=55 (chocolate)
C+D+E+G=59 (strawberry)
G=30 (all three flavours)
E=40 (chocolate and strawberry)
F=43 (vanilla and chocolate)
There may be mistakes or ambiguities in the question, but let's assume for the moment:
D=41 (vanilla and strawberry)
We need to discover whether the terminal 9 has any meaning.
E+F+G=30+40+43=113, which is in excess of 100, the total number of people. Therefore this is a misinterpretation of the figures, or there is a mistake in the figures.
Assume G=30 is correct. Then we can rewrite some equations:
A+D+F=26; B+E+F=25; C+D+E=29. Therefore D cannot be 41.
Let's further assume that:
E+G=40 instead of E=40, then E=10
F+G=43 instead of F=43, then F=13 and E+F+G=10+13+30=53.
From this it follows that B+E+F+G=55, so B=2.
C+D=29-10=19
D+G=41 (instead of D=41) so D=11, and C=8.
A=26-D-F=26-11-13=2.
So we have values for A, B, C, D, E, F, G so their sum is:
2+2+8+11+10+13+30=76 and H=24, implying that 24 people did not take any flavours.
The figures given in the question appear to contain errors. The question should be revised to correct any errors before a solution can be undertaken.