library(tidyverse)
library(readxl)
path = "Excel/665 Bi & Trimorphic Numbers.xlsx"
test = read_excel(path, range = "A1:A10")
# Only 1, 5, 6 and 0 squared and cubed give us the same digit at the end.
# so we can decrease the search scope.
df = data.frame(n = 1:100000) %>%
filter(n %% 10 %in% c(0, 1, 5, 6)) %>%
mutate(n2 = n^2, n3 = n^3) %>%
filter(str_ends(as.character(n2), as.character(n)),
str_ends(as.character(n3), as.character(n)))
all.equal(df$n, test$`Expected Answer`)
#> [1] TRUEExcel BI - Excel Challenge 665
excel-challenges
excel-formulas
🔰 Bi & Trimorphic Numbers - List numbers (n<100000) if n^3 and n^2 both end with n.
Challenge Description
🔰 Bi & Trimorphic Numbers - List numbers (n<100000) if n^3 and n^2 both end with n.
Solutions
- Logic: Read the workbook ranges needed for the challenge; Derive the required intermediate columns.
- Strengths: The code maps the workbook rule into a compact, reproducible pipeline.
- Areas for Improvement: The solution assumes the workbook layout and selected ranges remain stable, so any structural change in the sheet would require small adjustments.
- Gem: The elegant part is how little code is needed once the correct intermediate representation is chosen.
import pandas as pd
path = "665 Bi & Trimorphic Numbers.xlsx"
test = pd.read_excel(path, usecols="A", nrows=10)
# Only 1, 5, 6 and 0 squared and cubed give us the same digit at the end.
# so we can decrease the search scope.
df = pd.DataFrame({'n': range(1, 100001)})
df = df[df['n'].apply(lambda x: str(x)[-1] in ['0', '1', '5', '6'])]
df['n2'], df['n3'] = df['n'] ** 2, df['n'] ** 3
df['nlen'] = df['n'].astype(str).str.len()
df['n2m2'] = df.apply(lambda row: str(row['n2'])[-row['nlen']:] == str(row['n']), axis=1)
df['n3m3'] = df.apply(lambda row: str(row['n3'])[-row['nlen']:] == str(row['n']), axis=1)
df = df[df['n2m2'] & df['n3m3']].reset_index(drop=True)
df = df[['n']]
print(df['n'].equals(test['Expected Answer']))The Python version mirrors the same workbook logic with a concise, direct implementation.
Difficulty Level
Easy / Medium
The business rule is clear, though the workbook still needs a few transformation steps to reach the expected output.