# Complete numbers on Clock

I have a different kind of clock at my home. Image of Clock:

5 o'clock on this clock means 1 o'clock actually. Display of data in table:

Can you complete all the numbers on this clock by finding type of clock?

HINT 1:

As everyone going in wrong direction so its a hint to point you to right direction or to result:)

HINT 2: One more example data to reduce possibilities..

HINT 3:

It works around display of numbers...

• hmm... hands of the clock are so weird. – Jamal Senjaya Dec 20 '17 at 5:14
• hey, i notice something different on hint 1, is it an infinite symbol (on bottom side)? – athin Dec 21 '17 at 11:12
• @athin, its not infinite symbol, think another way:) – Preet Dec 22 '17 at 0:20

Ok, i think i got it now.

The numbers are based on their 7-segment displays

Where a number's value is equal to the sum of all lit-up segments

For example, with 1:

So [1] = 2 + 3 = 5.

We can see that it applies to every other revealed number too:
[2] = 1 + 2 + 7 + 5 + 4 = 19.
[7] = 1 + 2 + 3 = 6.

For numbers with more than one digit, do this for both digits and sum their totals.
[11] = [1] + [1] = 5 + 5 = 10
[12] = [1] + [2] = 5 + 19 = 24

Doing this for all numbers, we get

• You definitely got it...! – Preet Dec 27 '17 at 2:40
• I can't believe i didnt notice that [11] = [1]+[1] and [12] = [1]+[2] from the table! Had to wait for that last hint before things finally connect :P – votbear Dec 27 '17 at 2:51

I assumed 19[2] + 5[1] = 24[12]

so concluded 24[12] - 10[11] = 14[10]

24[12]/4 = 6[3] -- 1/4th of 24

24[12]/2 = 12[6] -- half of 24

24[12]/4*3 = 18[9] -- 3/4th of 24

19[2] + 6[3] = 25[4]

18[9] + 14[10] = 32[8]

32[8] - 12[6] = 20[7]

25[8] - 12[6] = 13[5]

Reasons for different calculations:

Value for 3, 6, 9 based on 24 by dividing the clock in 4 quarters

The 3 points of black triangle are points that have total values.

The 3 points of blue triangle add value of next point to it to get the total of nearest black point value clock wise and anti-clockwise.

• I am new here :) please tell me the reason while downvoting – Mehravish Temkar Dec 20 '17 at 7:42
• Can you explain the thoughts behind your answer? Why is it that you use division for [3], [6], [9], [12], but then switched to additions and subtractions? Why is [2]+[3] = [4] but then [9]+[10]=[8]? and [8]-[6]=[7]? For me it looks like you're just randomly mashing the numbers you have together to fill all the slots with no rhyme or reason – votbear Dec 20 '17 at 7:44
• I'll try to explain @VotBear – Mehravish Temkar Dec 20 '17 at 7:46
• @Mehravish Temkar, Thanks for trying but sorry to say you are not on right track, what i can say is you don,t need to assume numbers or finding any relationships between both clocks like this. – Preet Dec 20 '17 at 7:50
• I see that in your clock, [12], [4] and [8] are the sums of the two numbers after/before them. But i can't figure out how you can get to this conclusion based on the initial question... – votbear Dec 20 '17 at 7:50

It seems the difference between each subsequent hour is 14, but since hour 11 on your clock has a lower value than earlier hours, I figured that there might be a modulo operation being applied. The modulo divisor needed to produce 10 by the hour 11 and also had to be greater than 24 which is the value of hour 12. The lowest possible one that worked was 27. So the formula for your clock, given hour n on a normal clock, is $(14*(n - 1) + 5)\ \%\ 27$. That said, since there are other modulo divisor's that work the correct answer is probably something more clever than this.