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Author SHA1 Message Date
David Leal
47b3c72982
docs: add the other/miscellaneous form (#8163)
Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: Dhruv Manilawala <dhruvmanila@gmail.com>
2023-03-14 11:16:52 +05:30
Maxim Smolskiy
9701e459e8
Add Project Euler problem 100 solution 1 (#8175)
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
2023-03-14 11:09:36 +05:30
4 changed files with 69 additions and 0 deletions

19
.github/ISSUE_TEMPLATE/other.yml vendored Normal file
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name: Other
description: Use this for any other issues. PLEASE do not create blank issues
labels: ["awaiting triage"]
body:
- type: textarea
id: issuedescription
attributes:
label: What would you like to share?
description: Provide a clear and concise explanation of your issue.
validations:
required: true
- type: textarea
id: extrainfo
attributes:
label: Additional information
description: Is there anything else we should know about this issue?
validations:
required: false

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@ -937,6 +937,8 @@
* [Sol1](project_euler/problem_097/sol1.py)
* Problem 099
* [Sol1](project_euler/problem_099/sol1.py)
* Problem 100
* [Sol1](project_euler/problem_100/sol1.py)
* Problem 101
* [Sol1](project_euler/problem_101/sol1.py)
* Problem 102

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"""
Project Euler Problem 100: https://projecteuler.net/problem=100
If a box contains twenty-one coloured discs, composed of fifteen blue discs and
six red discs, and two discs were taken at random, it can be seen that
the probability of taking two blue discs, P(BB) = (15/21) x (14/20) = 1/2.
The next such arrangement, for which there is exactly 50% chance of taking two blue
discs at random, is a box containing eighty-five blue discs and thirty-five red discs.
By finding the first arrangement to contain over 10^12 = 1,000,000,000,000 discs
in total, determine the number of blue discs that the box would contain.
"""
def solution(min_total: int = 10**12) -> int:
"""
Returns the number of blue discs for the first arrangement to contain
over min_total discs in total
>>> solution(2)
3
>>> solution(4)
15
>>> solution(21)
85
"""
prev_numerator = 1
prev_denominator = 0
numerator = 1
denominator = 1
while numerator <= 2 * min_total - 1:
prev_numerator += 2 * numerator
numerator += 2 * prev_numerator
prev_denominator += 2 * denominator
denominator += 2 * prev_denominator
return (denominator + 1) // 2
if __name__ == "__main__":
print(f"{solution() = }")