Counting Fingers

June 16, 2020

A little girl counts on her fingers in a curious way. She counts 1 on her thumb, 2 on her index finger, 3 on her middle finger, 4 on her ring finger, and 5 on her pinkie finger, then works back, counting 6 on her ring finger, 7 on her middle finger, 8 on her index finger, and 9 on her thumb, when she again turns around and counts 10 on her index finger, 11 on her middle finger, and so on.

Your task is to write a program that determines which finger the little girl will be on when she reaches a thousand. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.


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14 Responses to “Counting Fingers”

  1. matthew said

    I presume that should be: “counts 10 on her index finger, 11 on her middle finger, and so on”

  2. programmingpraxis said

    Correct. Fixed. Thank you.

  3. Zack said

    Here is my take on Julia:

    Cool drill for getting acquainted with modulo arithmetic. Cheers!

  4. Mark said
  5. Jan Van lent said
    f = lambda n: 4-abs(4-(n-1)%8)
    print("timrp"[f(1000)]) # see Mark's solution
  6. Xero said

    My thorouhly documented solution implemented in SML can be found at <ahref=””>. It takes a different approach from modular arithmetic.

  7. Maksym Fedenko said

    Hi, I’m beginner, can I resolve task in this way?

    public class Exercises1 {
    public static void main(String[] args) {
    Solution solution = new Solution();
    while (solution.getCounter_fingers() < 1006586890){
    solution.setCounter_fingers(solution.getCounter_fingers() + 4);
    solution.setCounter_iterations(solution.getCounter_iterations() + 1);
    solution.setCounter_fingers(solution.getCounter_fingers() – 1);
    if(solution.getCounter_iterations() % 2 == 0){
    System.out.println(“Girl stop count on index finger”);
    }else {
    System.out.println(“Girl stop count on ring finger”);

    public static class Solution {
        private int counter_fingers = 5;
        private int counter_iterations = 1;
        public int getCounter_fingers() {
            return counter_fingers;
        public void setCounter_fingers(int counter_fingers){
            this.counter_fingers = counter_fingers;
        public int getCounter_iterations() {
            return counter_iterations;
        public void setCounter_iterations(int counter_iterations) {
            this.counter_iterations = counter_iterations;
  8. Larry Lee said

    Using Spanish abbreviations for finger names (Haskell): finger n = ['i', 'p', 'i', 'm', 'a', 'c', 'a', 'm'] !! (nmod8)

  9. Here’s Clojure solution with infinity lazy sequence of fingers :)

    (defn counting-fingers [n]
      (let [fingers (cycle [:thumb :index :middle :ring
                            :pinky :ring :middle :index])]
        (first (drop (dec n) fingers))))
  10. (defn counting-fingers [n]
      ([:thumb :index :middle :ring
        :pinky :ring :middle :index] (mod (dec n) 8)))
  11. Daniel said

    Here’s a solution in C.

    #include <assert.h>
    #include <stdio.h>
    #include <stdlib.h>
    int main(int argc, char* argv[]) {
      assert(argc == 2);
      int x = atoi(argv[1]);
      assert(x > 0);
      char finger = "timrprmi"[(x - 1) % 8];
      printf("%c\n", finger);
      return EXIT_SUCCESS;


    $ ./a.out 1000
  12. Antonio Leonti said

    I took a very different approach from you all– my original thought was to just use x%8, but I decided to instead use the absolute value of a triangle wave. At least I thought it was neat.

    int finger(int x){
        return (int)(fabs(8/M_PI * asin(sin(M_PI*(x-1) / 8)))+0.5);
    int main(){
        printf("%c\n", "TIMRP"[finger(1000)]);
  13. Daniel said

    Here’s a Python solution inspired by @Antonio’s solution, adapted to use integers in place of floating point.

    def finger(x):
        return 'timrp'[abs(8 * ((x + 3) // 8) - x + 1)]
    for x in range(1, 11):
        print(x, finger(x))
    print(1000, finger(1000))


    1 t
    2 i
    3 m
    4 r
    5 p
    6 r
    7 m
    8 i
    9 t
    10 i
    1000 i
  14. Hakan said

    In my approach, I took advantage of array pointers in PHP. Every time the pointer reaches an outer finger (thumb/pinky), the array elements are reversed in order. You simply scroll down to see the finger that is declared at count number 1000.

    // Put your fingers in the array
    $fingers = [
    for ($i = 1; $i <= 1000; $i++) { 
    	// Declare both the count and finger with each iteration
    	echo $i.". ".current($fingers)."<br>";
    	// Move the array pointer up one element
    	// If the array pointer is at either the pinky or the thumb
    	if (current($fingers) == 'pinky' || current($fingers) == 'thumb') {
    		// reverse the order of the elements in the array
    		$fingers = array_reverse($fingers);

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