Divide the face of the clock into three parts with two lines so that the sum of the numbers in the three parts are equal.

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msrobinsonlovesalgebra's profile pic

msrobinsonlovesalgebra | High School Teacher | (Level 1) Adjunct Educator

Posted on

The sum of the numbers on the clock would be 78 (1 + 2 + 3 . . + 12).  So 78/3 = 26 so you would have to find the number combinations that would give you 26.  The only three combinations that work for a clock face are:

11 + 12 + 1 + 2

10 + 9 + 3 + 4

8 + 7 + 6 + 5

that means you will draw one line below the 11 and across to below the 2 and the second line would be above the 8 and across to below the 4. 

Seeing is believing . . .draw and label a clock face then add the two lines! 

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

Let P be a point between 10 and 11

Let Q be a point between  2and 3

Draw the chord PQ.

Let R be a point between 8 and 9 and S be a point between  4 and 5, Join the chord RS

Now the face of the clock has 3 regions.  The sector bounded by the chord PQ and its arch ,  the region PQSR   ,  and the region enclosed between the chord RS and its arch  containing numbers respectively: (2,1,,12,and 11) , (3, 4, 10 and  9 )  and (8, 7, 6 and 5)  in each regions so divided. The sum in each part or region is  26.

If the the clock has 12 not marked , then it could be treated as  zero and then clock face contains 1 to 11 and a  no number or zero. Under this situation,  [1, 0 (or no number),  11  , 10] , [3,  2,  9,  8] and [7,  6,  5   4] are the  numbers in the 3 regions separated by two chord PQ ( P in between  9 and 10 ,  Q is in between 1 and 2)  and RS (R is in between 7 and 8,     and S between  3 and 4). In this case the total of numbers in each region is 22.

krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

A clock has twelve numbers - 1 to 12. Sum of these twelve numbers is 78.

That is 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 = 78

we need to divide face of the clock drawing two lines that will divide face of the clock in three parts such that sum of numbers in each parts will be equal.

Therefore sum of number in each part should be 78/3 = 26.

This can be achieved by dividing the clock in three parts by two horizontal lines that divide the clock in three parts.

The top part will contain the numbers 1, 2, 11 and 12.

The second part in middle will contain numbers 3, 4, 9 and 10.

The lowest part will contain the numbers 5, 6, 7 and 8.

 

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