Ken's Puzzle of the Week
Sequential Digits on a Clock
- How many times in a 12-hour period (i.e. 1:00:00 to 12:59:59) can four
sequential digits be read on a digital clock? For example, 11:23:40 shows
"1234". Five Digits? Six? Zeros may be the first digit in
a sequence, but not the first digit on the display.
- Same question over 24 hours on a 24-hour clock (1:00:00 to 24:59:59).
Source: Original.
Solutions were received from Denis Borris, Claudio Baiocchi, and K Sengupta.
Denis' solutions are below.
LEFT-CENTER-RIGHT refers to position of the consecutives in the time number;
brackets are to "shorten the typing!"; ie 1:23:4(0-9) means 1:23:40,
1:23:41, ...1:23:49.
HOURS 1 - 9
==========
4 consecutives:
LEFT
1:23:4 (0-9) = 10
2:34:5 (0-9) = 10 : total 20
RIGHT
(1-9) 01:23 = 9
(1-9) 12:34 = 9
(1-9) 23:45 = 9
(1-9) 34:56 = 9 : total 36 : grand total 56
5 consecutive:
1:23:45
2:34:56
Of course, these both contain two "4 consecutives", all included in the
56 above.
Looked HARD, but couldn't find any "6 consecutives" [in the first 9
hours] !!
HOURS 10 - 24
===========
4 consecutives:
LEFT
12:34 (0-59) = 60
23:45 (0-59) = 60 : total 120
CENTER
(1-2) 0:12:3 (0-9) = 20
(1-2) 1:23:4 (0-9) = 20
(1-2) 2:34:5 (0-9) = 20 : total 60
RIGHT
(10-24):01:23 = 15
(10-24):12:34 = 15
(10-24):23:45 = 15
(10-24):34:56 = 15 : total 60 : grand total 240
5 consecutive:
LEFT
12:34:5(0-9) = 10 : total 10
RIGHT
(1-2)0:12:34 = 2
(1-2)1:23:45 = 2
(1-2)2:34:56 = 2 : total 6 : grand total 16
Of course, each contains two "4 consecutives", all included in the 240
above
6 consecutive:
12:34:56
Of course, contains two "5 consecutives", all included in the 16 above
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