Task — Valid times

You are given a time in the form ‘HH:MM’. The earliest possible time is ‘00:00’ and the latest possible time is ‘23:59’. In the string time, the digits represented by the ‘?’ symbol are unknown, and must be replaced with a digit from 0 to 9.

Write a script to return the count different ways we can make it a valid time.

Examples

Example 1
Input: $time = '?2:34'
Output: 3
0 -> '02:34' valid
1 -> '12:34' valid
2 -> '22:34' valid

Example 2
Input: $time = '?4:?0'
Output: 12
Hours: tens digit ?, ones digit 4 -> can be 04,
   and 14 (2 possibilities)
Minutes: tens digit ?,
   ones digit 0 -> tens can be 0-5 (6 possibilities)
Total: 2 × 6 = 12

Example 3
Input: $time = '??:??'
Output: 1440
Hours: from 00 to 23 -> 24 possibilities
Minutes: from 00 to 59 -> 60 possibilities
Total: 24 × 60 = 1440

Example 4
Input: $time = '?3:45'
Output: 3
If tens digit is 0 or 1 -> any ones digit works,
   so 03 and 13 are valid
If tens digit is 2 -> ones digit must be 0-3,
   but here ones digit is 3, so 23 is valid
Therefore: 0,1,2 are all valid -> 3 possibilities

Example 5
Input: $time = '2?:15'
Output: 4
Tens digit is 2, so hours can be 20-23
Ones digit can be 0,1,2,3 (4 possibilities)
Therefore: 4 valid times

Analysis

This is a great challenge in that itis simple to explain but quite tricky to solve.

The minutes are fairly easy: if the first character is '?' then there are 6 possibilities (0-5), and if the second is '?' there are 10 (0-9). These are independent, so overall there are 60 possibilities for '??';

The hours are trickier because there are 5 patteerns to consider:

• '?' followed by 4-9 has 2 possible values (0 or 1)
• '?' followed by 0-3 has 3 possibles (0, 1 or 2)
• '2' followed by '?' yields 4 possibilities (0, 1, 2 or 3)
• '0' or '1' followed by '?' can be any digit, ie 10 possibilities
• '??' has 24 possibles (00-23)

If there are multiple '?'s the numbers of possibilities have to be multiplied together.

And for a problem like this it's always sensible to check the premise that the input is valid, so I did that.

Try it 

#!/usr/bin/perl

# Blog: http://ccgi.campbellsmiths.force9.co.uk/challenge

use v5.26;    # The Weekly Challenge - 2026-03-23
use utf8;     # Week 366 - task 2 - Valid times
use warnings; # Peter Campbell Smith
binmode STDOUT, ':utf8';
use Encode;

valid_times('??:??');
valid_times('12:34');
valid_times('?2:34');
valid_times('1?:34');
valid_times('12:?4');
valid_times('12:3?');
valid_times('?7:00');
valid_times('24:00');

sub valid_times {
    
    my ($time, @d, $output, $hrs, $check);
    
    # initialise
    $time = $_[0];
    say qq[\nInput:  '$time'];
    
    # validate
    $check = $time;
    $check =~ s|\?|0|g;
    if ($check !~ m|^(\d\d):(\d\d)$| or $1 > 23 or $2 > 59) {
        say 'Output: invalid time';
        return;
    }
    
    # calculate result - mins
    @d = $time =~ m|^([012\?])([0-9\?]):([0-5\?])([0-9\?])$|;
    $output = 1;
    $output *= 10 if $d[3] eq '?';
    $output *= 6  if $d[2] eq '?';
    
    # and hrs
    $hrs = $d[0] . $d[1];
    $output *= 2  if $hrs =~ m|\?[4-9]|;
    $output *= 3  if $hrs =~ m|\?[0-3]|;
    $output *= 4  if $hrs =~ m|2\?|;
    $output *= 10 if $hrs =~ m|[01]\?|;
    $output *= 24 if $hrs =~ m|\?\?|;
    
    say qq[Output: $output];
}

last updated 2026-03-23 — 20 lines of code

Output

Input:  '??:??'
Output: 1440

Input:  '12:34'
Output: 1

Input:  '?2:34'
Output: 3

Input:  '1?:34'
Output: 10

Input:  '12:?4'
Output: 6

Input:  '12:3?'
Output: 10

Input:  '?7:00'
Output: 2

Input:  '24:00'
Output: invalid time