Question

60. If the letters A, B, C, D, E, F represent the numbers 1 to 6 in some order, and A + B = C = B + C = D C + E = F Then what number does C represent?

Answer 1

Using the given equations and the fact that A, B, C, D, E, and F are greater than zero, we can set the following inequalities:

`\begin{gathered} C>A, \\ C>B, \\ D>B, \\ D>C, \\ F>C, \\ F>E\text{.} \end{gathered}`

Therefore, C is greater than 2 numbers of the list and smaller than 2 numbers on the list, then C could be 3 or 4.

Substituting the first equation in the third equation we get:

`A+B+E=F\text{.}`

Therefore:

`F\ge6.`

Since F is an integer greater or equal than 1 and smaller or equal than 6, necessarily F=6.

Now, If C=3, from the third equation we get that E=3, which is false because the 6 letters represent different numbers. Therefore C=4.

Answer: C represents 4.