@venda said
@BigDoggProblem
You have the correct answer.
Well done!!
A 24 hour digital clock shows each digit using a 7 segment display.The digits 0-9 use 6,2,5,5,4,5,6,3,7,6 segments respectively.Starting from 00:00, how many times a day does the display change but still have the same total number of segments in use?
Good luck.
I don't even understand the question!!
There are no typo's -I've checked it 3 times
My solution:
Net change in segments for each possible digit change:
0 to 1: -4
1 to 2: +3
2 to 3: 0
3 to 4: -1
4 to 5: +1
5 to 6: +1
6 to 7: -3
7 to 8: +4
8 to 9: -1
9 to 0: 0
5 to 0: +1 [thanks, Babylonians!]
There are several different types of time change that do not change the total number of segments.
I) the least significant digit changes from 2 to 3
This happens six times every hour [..02 to ..03, ..13 to ..23, ..., ..52 to ..53].
6 x 24 = 144
II) changes involving ...9 to ...0
This causes the tens digit to change also. The only change that works is ..29 to ..30. It happens once per hour.
1 x 24 = 24
III) changes involving ..59 to ..00
There are exactly four that work.
0359 to 0400; 0859 to 0900; 1359 to 1400; 1859 to 1900
Answer: 144 + 24 + 4 =
172
I verified my answer using Python. For those interested in coding: https://repl.it/repls/FloweryChiefResource