Puzzles no. 424–418

Puzzles

Author: ExcelBI

All files (xlsx with puzzle and R with solution) for each and every puzzle are available on my Github. Enjoy.

Puzzle #414

I wonder if you know that big ships has identification number just like cars. This number is called IMO (International Maritime Organization) Number. It has specific structure and last digit is always control sum digit. Our challenge today is all about such numbers. Somehow in each number there is one character (digit in this case) missed. We need to find out and retrieve it.

IMO Number of a Vessel — This is a 7 digit number where last digit is check digit.
Check digit is calculated by multiplying first 6 digits (left to right) from 7 to 2 respectively, sum them and taking the last digit of the result.
Ex. 805353 = 8*7+0*6+5*5+3*4+5*3+3*2 = 114 = Last digit is 4.
Hence, IMO number is 8053534.
From the given IMO numbers, one digit is missing which is denoted by X.
Work out the complete IMO numbers.

Load libraries and data

library(tidyverse)
library(readxl)

input = read_excel("Excel/414 IMO Number of a Vessel.xlsx", range = "A1:A10") %>%
  filter(!`IMO Number` %in% c("36X7567", "41X6584")) 
test  = read_excel("Excel/414 IMO Number of a Vessel.xlsx", range = "A1:B10") %>%
  filter(!`IMO Number` %in% c("36X7567", "41X6584"))

# I am filtering those two numbers because they do not have single solution

Transformation

find_missing_digit = function(x) {
  digits = as.character(x) %>%
    str_split("") %>%
    unlist()

  pos = which(digits == "X")
  mults = 7:1
  
  if (pos == 7) {
    missing = sum(as.numeric(digits[1:6]) * mults[1:6]) %% 10 %>% as.character()
  }  
  else {
    missing_mult = 8 - pos
    checking_number = digits[7]
    df = data.frame(digits = digits[-pos], mults = mults[-pos]) %>%
      mutate(digits = as.numeric(digits)) %>%
      filter(mults != 1) %>%
      mutate(multiplicated = digits * mults) %>%
      summarise(sum = sum(multiplicated)) %>%
      pull()
    
    missing = data.frame(digits = 0:9, ch = checking_number, mm = missing_mult, sum = df) %>%
      mutate(sum = (sum + (digits * missing_mult)) %% 10,
             check = sum == ch) %>%
      filter(check) %>%
      select(digits) %>%
      pull() %>%
      as.character()
    }
  
  result = str_replace(x, "X", missing) %>% as.numeric()
  return(result)
}

result = input %>%
  mutate(`Answer Expected` = map_dbl(`IMO Number`, find_missing_digit)) 

Validation

identical(result, test)
# [1] TRUE

Puzzle #415

You wonder what is this weird ilustration above. This time we have to find cyclops numbers again (meaning that has only one 0 and it is placed in center of number), but not just cyclops number, but triangular cyclops number. What triangular means? Triangular number is a number where you can place this number of objects in triangle (like bowling pins or balls in 8-ball pool). So we need to find numbers that meet both conditions, exactly first 100 of them.

A Cyclops number is a number that has a zero in the center (so, it needs to have odd number of digits and >=3 digits). The 0 should not appear anywhere else other than in center. Hence, 12035 is a Cyclops number but 12005 is not as there are more than one 0s.
Nth Triangular number is calculated by N(N+1)/2. Hence, 1, 3, 6, 10, 15….are Triangular numbers.
Find the list of first 100 Cyclops Triangular numbers i.e. which are both Cyclops as well as Triangular.

Loading libraries and data

library(tidyverse)
library(readxl)

test = read_excel("Excel/415 Triangular Cyclops Numbers.xlsx", range = "A1:A101" )

Transformation

range = 1:1e7

is_triangular <- function(x) {
  n <- (-1 + sqrt(1 + 8 * x)) / 2
  n == floor(n)
}

r = data.frame(n = range) %>%
  mutate(nchar = nchar(n)) %>%
  filter(nchar %% 2 == 1) %>%
  mutate(zeroes = str_count(n, "0"), 
         central = substr(n, nchar/2+1, nchar/2+1)) %>%
  filter(zeroes == 1, 
         central == "0") %>%
  mutate(triangular = is_triangular(n)) %>%
  filter(triangular == TRUE) %>%
  head(100) %>%
  mutate(n = as.numeric(n))

Validation

identical(r$n, test$`Expect Answer`)
# [1] TRUE

Puzzle #416

Books, especially scientific ones, have very complicated multi-level table of contents. Some chapters are divided into subchapters, sub-subchapters or even deeper. This time we have kinda structure of book as an input. If there is one X, we have first level chapter, then two X’s subchapter, and so on. We need to make outline for TOC basing on those X’s. Not really hard I think.

Generate the number outlining.
If single X — 1, 2, 3…
If double X — 1.1, 1.2…
If triple x — 1.1.1. 1.1.2…

Load libraries and data

library(tidyverse)
library(readxl)

input = read_excel("Excel/416 Outline Numbering.xlsx", range = "A1:A20")
test  = read_excel("Excel/416 Outline Numbering.xlsx", range = "B1:B20")

Transformation

result = input %>%
  mutate(level = str_count(Strings, "X")) %>%
  mutate(first_lev = cumsum(level == 1)) %>%
  mutate(second_level = cumsum(level == 2), .by = first_lev) %>%
  mutate(third_level = cumsum(level == 3), .by = c(first_lev, second_level)) %>%
  mutate(`Answer Expected` = case_when(
    level == 1 ~ paste0(first_lev),
    level == 2 ~ paste0(first_lev, ".", second_level),
    level == 3 ~ paste0(first_lev, ".", second_level, ".", third_level)
  )) %>%
  select(`Answer Expected`)

Validation

identical(result, test)    
# [1] TRUE

Puzzle #417

Segregation has many conotations, but today we only have to separate digits from letters. Easy peasy. Lets try it out.

Split the given strings whenever a changeover happens between English alphabets and numbers.
Ex. d46c8a — d, 46, c, 8, a

Load libraries and data

library(tidyverse)
library(readxl)

input = read_excel("Excel/417 Split Alphabets and Numbers.xlsx", range = "A1:A10")
test  = read_excel("Excel/417 Split Alphabets and Numbers.xlsx", range = "B1:B10")

Transformation

pattern = ("[A-Za-z]+|[0-9]+")

result = input %>%
  mutate(splitted = map_chr(Data, ~str_extract_all(., pattern) %>% unlist() %>% 
                          str_c(collapse = ", "))) 

Validation

identical(result$splitted, test$`Expected Answer`)
# [1] TRUE

Puzzle #418

It looks like we need to check how long person works basing on reads from Work Time Registration System. Technically, we need to pivot table to have minimal and maximal time per person and day thrown to columns. Let’s try.

Pivot the given table for Date / Emp ID combinations with Min and Max Time. Min Time and Max Time will appear in alternate rows. First Min time will appear and then Max time in other row will appear.

Load libraries and data

library(tidyverse)
library(readxl)
library(hms)

input = read_excel("Excel/418 Pivot on Min and Max .xlsx", range = "A1:C26")
test  = read_excel("Excel/418 Pivot on Min and Max .xlsx", range = "E1:G13") %>%
  mutate(`Min & Max Time` = as_hms(`Min & Max Time`))

Transformation

result = input %>%
  summarise(Min = min(Time), Max = max(Time), .by = c(Date, `Emp ID`)) %>%
  pivot_longer(cols = c(Min, Max), names_to = "Type", values_to = "Time") %>%
  mutate(`Min & Max Time` = as_hms(Time)) %>%
  select(-c(Type, Time)) %>%
  arrange(Date, `Emp ID`)

Validation

identical(result, test)
# [1] TRUE

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