Can you divide a clock with 2 lines, so the sum of the hour numbers in each section are the same?

Can you divide a clock, with 2 lines, so that the sum of the hour number in each of the 3 sections is the same?


I think each section has to equal 26?Can you divide a clock with 2 lines, so the sum of the hour numbers in each section are the same?
The sum of 1+2+3+...+12 = 12(13)/2 = 78. So if all three sections add up to this number, then yes, they have to be 78/3 = 26.





Notice that when you draw these two lines to make three sections, at least one section is going to be made up of consecutive numbers. Starting with 12+11, you get 23. Adding the 10 gives you 33, which goes over. But the 1 is next to the 12, and 11+12+1+2 = 26. So maybe one section has the numbers ';11, 12, 1, 2';.





Continue again with 10+9=19. Adding the 8 gives 27, which goes over the limit. But adding from the other side gives 10+9+3+4 = 26. So those numbers make up the middle piece. This leaves ';5, 6, 7, 8'; as the third piece.Can you divide a clock with 2 lines, so the sum of the hour numbers in each section are the same?
first add up all the numbers to get 78. with 2 lines, you can get 4 segments, but that would mean that each section would need to have a total of 19.5, which is impossible with integers, so you would have three sections with 26 in each section.





as the numbers are in order, we can notice that if 10 and 11 are in the same group, they need a 5, which is next to neither, so they can not be in the same group. therefore, 10 and 9 must be in the same group, which gives 19, needing 7....which is not next to the 10 or the 9, so therefore there is no group for the 10 to fit in.





therefore, it is not possible with two lines to split a clock face into segments in which the amount of hours in each are equal.





i've just read googol's answer, and i would agree with it if the numbers did not need to be adjacent...
divide it diagonally down, so you get


11,12,1,2;


9,10,3,4;


5,6,7,8.