Excel BI - Excel Challenge 777

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excel-formulas

🔰 N Answer Expected Generate the triangles shown corresponding to number of rows shown in column A.

Published

March 24, 2026

Illustration for Excel BI - Excel Challenge 777

Challenge Description

🔰 N Answer Expected Generate the triangles shown corresponding to number of rows shown in column A.

Solutions

library(tidyverse)
library(readxl)

path = "Excel/700-799/777/777 Reverse Flyod Triangle.xlsx"
input1 = read_excel(path, range = "A2:A2", col_names = FALSE) %>% pull()
input2 = read_excel(path, range = "A5:A5", col_names = FALSE) %>% pull()
input3 = read_excel(path, range = "A9:A9", col_names = FALSE) %>% pull()
test1  = read_excel(path, range = "C2:D3", col_names = FALSE) %>% as.matrix()
test2  = read_excel(path, range = "C5:E7", col_names = FALSE) %>% as.matrix()
test3  = read_excel(path, range = "C9:L18", col_names = FALSE) %>% as.matrix()

tri_matrix = function(n) {
  M = matrix(NA, n, n)
  for (i in seq_len(n)) {
    M[i, 1:i] = rev(seq_len(i) + i * (i - 1) / 2)
  }
  M
}

all.equal(tri_matrix(input1), test1, check.attributes = FALSE) # TRUE
all.equal(tri_matrix(input2), test2, check.attributes = FALSE) # TRUE
all.equal(tri_matrix(input3), test3, check.attributes = FALSE) # TRUE

Logic: Read the workbook ranges needed for the challenge; Iterate through the sequence until the rule is satisfied.
Strengths: The algorithm is explicit about the sequence rule, so the control flow is easy to validate against the prompt.
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 non-obvious part is the local rule inside the loop, because that rule determines the whole output.

import pandas as pd
import numpy as np

path = "700-799/777/777 Reverse Flyod Triangle.xlsx"

input1 = pd.read_excel(path, usecols="A", skiprows=1, nrows=1, header=None).iloc[0, 0]
input2 = pd.read_excel(path, usecols="A", skiprows=4, nrows=1, header=None).iloc[0, 0]
input3 = pd.read_excel(path, usecols="A", skiprows=8, nrows=1, header=None).iloc[0, 0]

test1 = pd.read_excel(path, usecols="C:D", skiprows=1, nrows=2, header=None).values
test2 = pd.read_excel(path, usecols="C:E", skiprows=4, nrows=3, header=None).values
test3 = pd.read_excel(path, usecols="C:L", skiprows=8, nrows=10, header=None).values

def tri_matrix(n):
    mat = np.full((n, n), np.nan)
    for i in range(n):
        start = (i + 1) * (i + 2) // 2
        mat[i, :i+1] = np.arange(start, start - i - 1, -1)
    return mat

print(np.array_equal(tri_matrix(input1), test1, equal_nan=True)) # True
print(np.array_equal(tri_matrix(input2), test2, equal_nan=True)) # True
print(np.array_equal(tri_matrix(input3), test3, equal_nan=True)) # True

The Python version keeps the algorithm explicit, which helps when the challenge depends on a greedy or iterative rule.

Difficulty Level

Easy / Medium

The business rule is clear, though the workbook still needs a few transformation steps to reach the expected output.