# Seven letters riddle

Hoping it is a never-seen riddle, here is the problem.

We have seven letters A,B,C,D,E,F,G. Each letter is associated with a unique number between 1 and 10. We know the following:

• D is 3 units smaller than A
• B is the number in the middle
• A is two units greater than B
• F is smaller than B about the same quantity C is greater than D
• G is greater than F
• The numbers are consecutive

Which is the fifth number (i.e. letter) in ascending order?

This is my solution: From the first three properties with the last one, we draw the relative scenario in this way

_ _ D B _ A _


Now, F < B. Clearly, F cannot lie in the first position, otherwise, C would replace A because of the fourth condition. Hence,

_ F D B C A _


Now it's all done I think. The answer is C

What do you think about it? Is this a good reasoning? Do you propose other solutions?

• Looks good to me! Commented Feb 18, 2021 at 12:56
• Welcome to Puzzling! Could you please add a reference to the puzzle? Commented Feb 18, 2021 at 13:34
• I would, but I red it during an interview, so I have no reference. Commented Feb 18, 2021 at 15:07

Since we did not use the condition that G is greater than F, we must check if there is no contradiction. Well, if we use this, we get the entire sequence as E F D B C A G (since G must come to some point after F), so the puzzle itself is non-contradictory. However, if that condition were incompatible with our previous deductions (for example, if it were "G is 2 units greater than F", we would get no space to place G), the puzzle would be unsolvable at all. So this last step is only to check the absence of contradictions in the puzzle itself.