Select the option that represents the letters that, when placed from left to right in the blanks below, will complete the letter series. D _ F D _ F _ F _ D _ F

Correct — C. Twelve places, five blanks, and one three-letter block repeated four times.

Rule: D F F repeated.

D is printed at places 1, 4 and 10 — every third place, so D opens each block. F is printed at 3, 6, 8 and 12, all of which are second or third slots.

Filling the blanks at 2, 5, 7, 9 and 11 with F F D F F gives D F F | D F F | D F F | D F F → option (c).

Why the others are wrong

• (a)
  D F D D F — Option (a) puts D at place 2, immediately after the D printed at place 1. The block D F F holds a single D, so two D's can never stand together.
• (b)
  D F F D D — Option (b) makes places 9, 10 and 11 read D D D — place 10 prints D and the option supplies D on both sides of it. A three-letter block cannot produce a run of three identical letters.
• (d)
  F D D F F — Option (d) puts D at place 5, right after the D printed at place 4. Same objection, one block later: the row would carry a doubled D that D F F cannot generate.

The row is a cyclic block, so a place's role is fixed by its position counted in threes. Establish the period before testing any option.

D appears at places 1, 4 and 10. The gaps are 3 and 6, so the period is 3, and places 1, 4, 7 and 10 all carry D while the remaining eight carry F.

Testing an option then costs one comparison per blank, and the first clash kills it.

Key facts

• The period is 3, fixed by the printed D's at places 1, 4 and 10.
• Places 1, 4, 7 and 10 carry D and every other place carries F.
• The completed row reads D F F D F F D F F D F F.
• There are five blanks, so the answer string is five letters long.

Common traps

• Looking for a pattern in the underscores instead of in the printed letters.
• Assuming the block must use both letters equally, which would force D F rather than D F F.
• Filling all five blanks before checking the first clash, which burns time under the section clock.

No directly related past PYQ was found.