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09 May 2026, 13:15
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The simplest way to solve it is algebraically:
We know that:
75+80+55−a−2b=100(1)
where a represents the number of people with exactly 2 devices and b the number of people with exactly 3 devices.
From (1), we have:
a+2b=110(2)
To maximize b, we set a=0.
Thus, b max =55
We also know that:
c+a+b=100(3)
where c represents the number of people with exactly 1 device.
From (2), we know that in order to minimize b, we want to maximize a.
To maximize a, we set c=0 in (3).
Therefore,
a+2b=110
and
a+b=100
Solving the linear system, we obtain:
b=10
Therefore, b min =10
Answer:
55−10=45.
We know that:
75+80+55−a−2b=100(1)
where a represents the number of people with exactly 2 devices and b the number of people with exactly 3 devices.
From (1), we have:
a+2b=110(2)
To maximize b, we set a=0.
Thus, b max =55
We also know that:
c+a+b=100(3)
where c represents the number of people with exactly 1 device.
From (2), we know that in order to minimize b, we want to maximize a.
To maximize a, we set c=0 in (3).
Therefore,
a+2b=110
and
a+b=100
Solving the linear system, we obtain:
b=10
Therefore, b min =10
Answer:
55−10=45.
09 May 2026, 13:27
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Also notice that the maximum triple intersection is limited by the smallest set, which in this case is 55.
juliansorre
15 May 2026, 07:49
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Hope this helps
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25 Jul 2026, 08:21
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After working through enough examples, I finally came up with two simple formulas to calculate the minimum and maximum values for three overlapping sets. I think they're correct, but I'd appreciate it if someone could point out any mistakes or suggest improvements.
Note: T-> Total/Union, ⌊x⌋ -> Represents the floor value
In the given question:
MAX(A, B, C) = min( min(75, 80, 55), ⌊ (75+80+55-100)/2) = min (55, 55) = 55
MIN(A, B, C) = max(0, 75+80+55-200) = max(0, 10) = 10
x = MAX
y = MIN
x - y = 55-10 = 45
Note: T-> Total/Union, ⌊x⌋ -> Represents the floor value
Quote:
In the given question:
MAX(A, B, C) = min( min(75, 80, 55), ⌊ (75+80+55-100)/2) = min (55, 55) = 55
MIN(A, B, C) = max(0, 75+80+55-200) = max(0, 10) = 10
x = MAX
y = MIN
x - y = 55-10 = 45
