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# help!!!

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Maria writes a number on each face of the cube. Then, for each corner point of the cube, she adds the numbers on the faces which meet at that corner. (For corner B she adds the numbers on faces BCDA, BAEF, and BFGC.) In this way, she gets a total of 14 for corner C, 16 for Corner D, and 24 for corner E. Which total, does she get for corner F?

May 12, 2020

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Maria writes a number on each face of the cube.

Then, for each corner point of the cube, she adds the numbers on the faces which meet at that corner.

(For corner B she adds the numbers on faces BCDA, BAEF, and BFGC).

In this way, she gets a total of 14 for corner C, 16 for Corner D, and 24 for corner E.

Which total, does she get for corner F?

$$\begin{array}{|lrcll|} \hline \text{corner D}: & 16 &=& f_2+f_3+f_5 \\ \text{corner C}: & 14 &=& f_3+f_4+f_5 \\ \hline & D-C &=& f_2+f_3+f_5-(f_3+f_4+f_5) \\ & 16-14 &=& f_2-f_4 \\ &\mathbf{ 2 } &=& \mathbf{ f_2-f_4 } \\ \hline \end{array}$$

$$\begin{array}{|lrcll|} \hline \text{corner F}: & F &=& f_1+f_4+f_6 \\ \text{corner E}: & 24 &=& f_1+f_2+f_6 \\ \hline & F-E &=& f_1+f_4+f_6-(f_1+f_2+f_6) \\ & F-24 &=& f_4-f_2 \\ & F &=& 24+ f_4-f_2 \\ & F &=& 24-( f_2-f_4) \quad | \quad \mathbf{ f_2-f_4=2} \\ & F &=& 24-2 \\ &\mathbf{ F } &=& \mathbf{ 22 } \\ \hline \end{array}$$

May 12, 2020