What is the maximum number of liars among them?
Calculus
Level
2
We wants to arrange the numbers 2, 3, 4, . . . , 10 into several groups such that the sum of the numbers in each group is the same. What is the largest number of groups he can get?
The answer is 3.
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1 solution
Sum = 9(2+10)/2 = 54
54 = 2¹ × 3³
The sum in our subgroups have to be the same AND each is at least equal to 10, the largest element that needs to be sorted. The smallest number larger than 10 that can be constructed as a product of { 2 , 3 , 3 , 3 } is 18, thus there must be 3 subgroups at most.