Digital Clock Brightness

Question

My alarm clock has a typical 7-segment digital display showing hours and minutes.

Every lit segment is equally bright, and every unlit segment is equally dark. The separator (:) is always lit.

Assuming the clock uses 12-hour time without a leading zero for the hours, at what time does the overall brightness (i.e., the total number of lit segments) of the display change the most?

Answer 1

Logic behind the answer:

The biggest change in brightness is: 7->8 (+4), 0->1 (-4), 1->2 (+3), 6->7 (-3).
Changing time by "tens," the greatest increase is from :19->:20 (+4), which is better than any single digit change.
An hour change (:59->:00) results in +1 brightness, so it is "inefficient" to go down in brightness (change in a single digit, 6->7, is less than :19->:20, and going from 6:59->7:00, is only a change of (-1)). So we are looking for an increase in brightness.

So, without really looking at anything else, my initial guess is:

7:59->8:00

resulting in:

+5 brightness

Note:

There is no lateral thinking tag, but when the clock is at 8:08, unplugging it results in a change of (-20) which is a greater change than (+6).

Edit:

Nine is 6 digits, not 5 like I originally thought.

Answer 2

The answer has already been given, but I show my approach how to get there, just a simple bash script brute-forcing all possibilities:

#!/bin/bash
brightness(){
    local b=0 c
    for ((c=0;c<${#1};c++)); do
    case ${1:$c:1} in
        0) (( b+=6 )); ;;
        1) (( b+=2 )); ;;
        2) (( b+=5 )); ;;
        3) (( b+=5 )); ;;
        4) (( b+=4 )); ;;
        5) (( b+=5 )); ;;
        6) (( b+=6 )); ;;
        7) (( b+=3 )); ;;
        8) (( b+=7 )); ;;
        9) (( b+=6 )); ;;
    esac
done
echo $b
}
biggest_diff=0
bbefore=$(brightness 1159)
for h in {0..11}; do
for m in {00..59}; do
    bnow=$(brightness $h$m)
        diff=$(( bnow - bbefore ))
    if [ ${diff#-} -ge $biggest_diff ]; then
        biggest_diff=${diff#-}
            echo Diff: $diff
        echo Time: $h:$m
    fi
    bbefore=$bnow
    done;
done

Calling it returns ...

./clock | tail -n2

Diff: 5
Time: 8:00

Answer 3

Well, it is

+5 brightness from:
7:59 to 8:00

Since:

total of 7:59 is 3 + 5 + 6 = 14
total of 8:00 is 7 + 6 + 6 = 19