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import math
if __name__ == '__main__':
a_target = 73
b_target = 58
c_target = 32
a, b, c = 0, 0, 0
a_percent, b_percent, c_percent = 0, 0, 0
total = 0
while a_percent != a_target or b_percent != b_target or c_percent != c_target:
# Perform one vote, to the option that is furthest from the target
a_diff = a_target - a_percent
b_diff = b_target - b_percent
c_diff = c_target - c_percent
if a_diff > 0:
# vote for a
a += 1
if b_diff > 0:
# vote for b
b += 1
if c_diff > 0:
# vote for c
c += 1
total += 1
# Recalculate all percents
a_percent = math.floor(a / total * 100)
b_percent = math.floor(b / total * 100)
c_percent = math.floor(c / total * 100)
print(f'A: {a} votes -> {a_percent}%')
print(f'B: {b} votes -> {b_percent}%')
print(f'C: {c} votes -> {c_percent}%')
print(total)
print(f'{a_percent}, {b_percent}, {c_percent}')
# time.sleep(5)
print(f'The number of people in office: {total}')
print(f'A: {a} votes - {a_percent}%')
print(f'B: {b} votes - {b_percent}%')
print(f'C: {c} votes - {c_percent}%')
A: 1 votes -> 100%
B: 1 votes -> 100%
C: 1 votes -> 100%
1
100, 100, 100
A: 1 votes -> 50%
B: 1 votes -> 50%
C: 1 votes -> 50%
2
50, 50, 50
A: 2 votes -> 66%
B: 2 votes -> 66%
C: 1 votes -> 33%
3
66, 66, 33
A: 3 votes -> 75%
B: 2 votes -> 50%
C: 1 votes -> 25%
4
75, 50, 25
A: 3 votes -> 60%
B: 3 votes -> 60%
C: 2 votes -> 40%
5
60, 60, 40
A: 4 votes -> 66%
B: 3 votes -> 50%
C: 2 votes -> 33%
6
66, 50, 33
A: 5 votes -> 71%
B: 4 votes -> 57%
C: 2 votes -> 28%
7
71, 57, 28
A: 6 votes -> 75%
B: 5 votes -> 62%
C: 3 votes -> 37%
8
75, 62, 37
A: 6 votes -> 66%
B: 5 votes -> 55%
C: 3 votes -> 33%
9
66, 55, 33
A: 7 votes -> 70%
B: 6 votes -> 60%
C: 3 votes -> 30%
10
70, 60, 30
A: 8 votes -> 72%
B: 6 votes -> 54%
C: 4 votes -> 36%
11
72, 54, 36
A: 9 votes -> 75%
B: 7 votes -> 58%
C: 4 votes -> 33%
12
75, 58, 33
A: 9 votes -> 69%
B: 7 votes -> 53%
C: 4 votes -> 30%
13
69, 53, 30
A: 10 votes -> 71%
B: 8 votes -> 57%
C: 5 votes -> 35%
14
71, 57, 35
A: 11 votes -> 73%
B: 9 votes -> 60%
C: 5 votes -> 33%
15
73, 60, 33
A: 11 votes -> 68%
B: 9 votes -> 56%
C: 5 votes -> 31%
16
68, 56, 31
A: 12 votes -> 70%
B: 10 votes -> 58%
C: 6 votes -> 35%
17
70, 58, 35
A: 13 votes -> 72%
B: 10 votes -> 55%
C: 6 votes -> 33%
18
72, 55, 33
A: 14 votes -> 73%
B: 11 votes -> 57%
C: 6 votes -> 31%
19
73, 57, 31
A: 14 votes -> 70%
B: 12 votes -> 60%
C: 7 votes -> 35%
20
70, 60, 35
A: 15 votes -> 71%
B: 12 votes -> 57%
C: 7 votes -> 33%
21
71, 57, 33
A: 16 votes -> 72%
B: 13 votes -> 59%
C: 7 votes -> 31%
22
72, 59, 31
A: 17 votes -> 73%
B: 13 votes -> 56%
C: 8 votes -> 34%
23
73, 56, 34
A: 17 votes -> 70%
B: 14 votes -> 58%
C: 8 votes -> 33%
24
70, 58, 33
A: 18 votes -> 72%
B: 14 votes -> 56%
C: 8 votes -> 32%
25
72, 56, 32
A: 19 votes -> 73%
B: 15 votes -> 57%
C: 8 votes -> 30%
26
73, 57, 30
A: 19 votes -> 70%
B: 16 votes -> 59%
C: 9 votes -> 33%
27
70, 59, 33
A: 20 votes -> 71%
B: 16 votes -> 57%
C: 9 votes -> 32%
28
71, 57, 32
A: 21 votes -> 72%
B: 17 votes -> 58%
C: 9 votes -> 31%
29
72, 58, 31
A: 22 votes -> 73%
B: 17 votes -> 56%
C: 10 votes -> 33%
30
73, 56, 33
A: 22 votes -> 70%
B: 18 votes -> 58%
C: 10 votes -> 32%
31
70, 58, 32
A: 23 votes -> 71%
B: 18 votes -> 56%
C: 10 votes -> 31%
32
71, 56, 31
A: 24 votes -> 72%
B: 19 votes -> 57%
C: 11 votes -> 33%
33
72, 57, 33
A: 25 votes -> 73%
B: 20 votes -> 58%
C: 11 votes -> 32%
34
73, 58, 32
The number of people in office: 34
A: 25 votes - 73%
B: 20 votes - 58%
C: 11 votes - 32%

Extra Credit

The following code counts down from 10000 until you find a number of coworkers that doesn't let you satisfy the percentages. We calculate the optimal number of votes by taking ceiling after calculating the target percentage, and multiplying by the number of coworkers. This value is the ideal number of votes (note it cannot be a non-whole number) cast for that holiday party option. Then, we divide by the total coworkers and take the floor to simulate writing down the percentage up to the decimal point. If this value is not equal to the target for each of the holiday options, then that number of coworkers does not contain a possible solution

Answer

By running the below code, we find that the largest number of coworkers where the percentages are not possible is 66.

Here's a list of all the impossible numbers of coworkers: 66, 54, 47, 44, 35, 33, 32, 27, 22, 21, 20, 18, 16, 14, 13, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1

import math
import numpy as np
if __name__ == '__main__':
coworkers = np.arange(100000, 0, -1)
a_target = 73
b_target = 58
c_target = 32
for t in coworkers:
# Choose an a that will get you as close as possible to the target
a = math.ceil(a_target / 100 * t)
b = math.ceil(b_target / 100 * t)
c = math.ceil(c_target / 100 * t)
a_percent = math.floor(a / t * 100)
b_percent = math.floor(b / t * 100)
c_percent = math.floor(c / t * 100)
if (a_percent != a_target and b_percent != b_target and c_percent != c_target):
print(f'Found the largest number of coworkers where it is impossible: {t}')
print(f'A = {a_percent}%')
print(f'B = {b_percent}%')
print(f'C = {c_percent}%')
break
Found the largest number of coworkers where it is impossible: 66
A = 74%
B = 59%
C = 33%
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