Guess my Number

Activator

Guess my number, explain how you came up with it:

• When divided by 2, my number has a remainder of 1.
• When divided by 3, my number has a remainder of 2.
• When divided by 4, my number has a remainder of 3.
• When divided by 5, my number has a remainder of 4.
• When divided by 6, my number has a remainder of 5.
• When divided by 7, my number has a remainder of 6.
• When divided by 8, my number has a remainder of 7.
• When divided by 9, my number has a remainder of 8.

My number is the smallest integer for which all above clues hold true.

Writing the function to find the number

# Function to find the number.
find_number <- function() {
  # Initialize the number
  num <- 1
  
  # Loop until we find the number that satisfies all the conditions
  while (TRUE) {
    # Check the conditions
    if (num %% 2 == 1 &&
        num %% 3 == 2 &&
        num %% 4 == 3 &&
        num %% 5 == 4 &&
        num %% 6 == 5 &&
        num %% 7 == 6 &&
        num %% 8 == 7 &&
        num %% 9 == 8) {
      return(num)
    }
    # Increment the number
    num <- num + 1
  }
}

Finding the number and proving result

Below we are calling the function and assigning the result to the variable x. The number that was found is 2519.

# Call the function
x <- find_number()

# Looking at the number found
print(x)

## [1] 2519

Now we will be proving that the result we got, 2519, is the correct answer. Below we will be dividing our result and the output will be the remainder.

# Checking if the result is true.
x %% 8

## [1] 7

x %% 7

## [1] 6

x %% 6

## [1] 5

x %% 5

## [1] 4

x %% 4

## [1] 3

x %% 3

## [1] 2

x %% 2

## [1] 1