Puzzle:

Take a look at the clock below. Break the clock into exactly five pieces such that sums of all the numbers on each piece are 8, 10, 12, 14 and 16.

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Solution:

Solution:

1+2+...+11+12 = 78 and 8+10+12+14+16 = 60. So you probably should try to decrease the total on the clock. How could you decrease the total without throwing away something? Have a good look at the numbers 10, 11 and 12. If you break the clock between the 1 and 2 of twelve, you loose 12 in the total but you gain 1 and 2. So overall the total would decrease by 9. Breaking between the 1 and 1 of 11 and between the 1 and 0 of 10 also decreases the total by 9. So if you break between two of the numbers 10, 11 and 12, the total will become 78-9-9 = 60.

## 3 comments:

here the sum of the numbers on all pieces is 60 which is not equal to sumof first 12 natural numbers

so leave the numbers on it and consider the no of minutes on it

as the total no of minutes on a dial is 60 so cut the dial at 8 min,20min,30min,44min,60min now every piece has required no of minutes on it

how can u cut at 60 min??? and all the pieces will be subset of the biggest cut...isnt it 5 different cuts?

this can be solved by diving no 12 and 10 into 1,2,1,0 resp...and sum of all no is 60 ...divide it into 5 parts as required

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