Two is better than one
Mike want to form two teams of equal skill values.
It starts with four people with different skills level: A = 1, B = 2, C = 3, D = 4.
He noticed that when two people work togheter there was an extra +1 skills bonus, when three people work togheter there was an extra +2 skill bonus, with three people the skill bonus is +3 and so on.
It divides the people in this way:
FIRST TEAM
A + D
total skills 1 + 4 + (1 bonus) = 6
SECOND TEAM
B + C
total skils 2 + 3 + (1 bonus) = 6
With his work Mike attract another person E with a skills level of 5 and so he must to reassemble in a different way the team to have equal skill values.
The new teams are:
FIRST TEAM
A + B + D total skills 1 + 2 + 4 + (2 bonus) = 9
SECOND TEAM
C + E
total skills 3 + 5 + (1 bonus) = 9
After several years, Mike have 9 people with increasing skills (A=1, B=2, C=3, D=4, E=5, F=6 ....)
What is the total skills of the two team ?
Hint: In previous examples was 6 and 9.
The answer is 26.
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1 solution
Even without knowing the right division, we know that the total some of the skills is 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 2 1 0 ∗ 9 = 45 than consider any division of 9 members, the total some of bonus skills is always 7. so Total skills is (45+7)/2 = 26