There are 6 people in the math and physics groups, and 4 people in the physics and chemistry groups. Each student can participate in at most two groups, and the number of people who participate in the physics group is 15, so the number of people who participate in the physics group alone is 15-6-4=5, as shown in the figure.

Suppose that the number of people who join the math group alone is S, the number of people who join the chemistry group alone is H, and the number of people who join the math and chemistry groups at the same time is X, then: S+X+6 = 26...( 1).

H+X+4= 13......(2)

S+H+X+ 15=36......(3)

Solutions of contingency (1), (2) and (3): S= 12, X=8, H= 1.

Therefore, eight students take part in the math and chemistry groups at the same time. ?

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