Omid - Challenge 360

data-challenges
advanced-exercises
🔰 In Table 1, extract all sub-matrices of size three which are symmetric.
Published

March 24, 2026

Illustration for Omid - Challenge 360

Challenge Description

🔰 In Table 1, extract all sub-matrices of size three which are symmetric.

Solutions

library(tidyverse)
library(readxl)

path <- "300-399/360/CH-360 Matrix Calculation.xlsx"
input <- read_excel(path, range = "C4:H9", col_names = FALSE) %>% as.matrix()
test1 <- read_excel(path, range = "K4:M6", col_names = FALSE) %>% as.matrix()
test2 <- read_excel(path, range = "P4:R6", col_names = FALSE) %>% as.matrix()
test3 <- read_excel(path, range = "U4:W6", col_names = FALSE) %>% as.matrix()

find_sym_submatrices <- function(mat, n) {
  r <- list()
  sz <- nrow(mat) - n + 1
  for (i in 1:sz) {
    for (j in 1:sz) {
      s <- mat[i:(i + n - 1), j:(j + n - 1)]
      if (all(s == t(s))) r[[length(r) + 1]] <- list(pos = c(i, j), mat = s)
    }
  }
  return(r)
}

res = find_sym_submatrices(input, 3)
all(res[[1]]$mat == test1) # TRUE
all(res[[4]]$mat == test2) # TRUE
all(res[[3]]$mat == test3) # TRUE

# one extra find
res[[2]]$mat

#      ...3 ...4 ...5
# [1,]    1    4    8
# [2,]    4    7    7
# [3,]    8    7    3

  • Logic:

    • Reads the workbook ranges needed for the challenge

    • Applies the rule iteratively until the output stabilizes

  • Strengths:

    • The R solution stays close to the workbook rule and keeps the transformation compact.

  • Areas for Improvement:

    • The code assumes the sheet structure and source ranges remain stable.

  • Gem:

    • The strongest part of the solution is choosing the right intermediate representation before shaping the final output.
import pandas as pd
import numpy as np

path = "300-399/360/CH-360 Matrix Calculation.xlsx"
input = pd.read_excel(path, usecols="C:H", skiprows=3, nrows=6, header=None).values
test1 = pd.read_excel(path, usecols="K:M", skiprows=3, nrows=3, header=None).values
test2 = pd.read_excel(path, usecols="P:R", skiprows=3, nrows=3, header=None).values
test3 = pd.read_excel(path, usecols="U:W", skiprows=3, nrows=3, header=None).values

def find_sym_submatrices(mat, n):
    r = []
    sz = mat.shape[0] - n + 1
    for i in range(sz):
        for j in range(sz):
            s = mat[i:i+n, j:j+n]
            if np.array_equal(s, s.T):
                r.append({'pos':(i,j), 'mat':s})
    return r

result = find_sym_submatrices(input, 3)

print((result[0]['mat'] == test1).all()) # True
print((result[3]['mat'] == test2).all()) # True
print((result[2]['mat'] == test3).all()) # True
# one extra symmetric matrix exists
print(result[1]['mat'])
# [[1 4 8]
#  [4 7 7]
#  [8 7 3]]

  • Logic:

    • Reads the workbook ranges needed for the challenge

    • Applies the rule iteratively until the output stabilizes

  • Strengths:

    • The Python version follows the same rule in a direct dataframe-oriented implementation.

  • Areas for Improvement:

    • The code assumes the workbook layout remains stable, so any sheet redesign would require small adjustments.

  • Gem:

    • The implementation stays close to the original workbook rule instead of adding unnecessary abstraction.

Difficulty Level

This task is moderate:

  • The business rule is readable, but the workbook still requires careful implementation to reach the expected layout.