Question

Shown below is a strip of paper which is folded multiple times. How many red pawns are placed on the same side of the paper as the blue pawn? 

Answer 1

Correct Answer: 9

Step 1: Note the blue pawn's position and count the folds lying between it and each red pawn.

Step 2: A red pawn shares the blue pawn's side only when an even number of folds separate them.

Step 3: Checking every red pawn this way and keeping the even-fold-count ones gives 9 pawns on the blue pawn's side.

Step 4: The rest sit an odd number of folds away and land on the opposite side. \[ \boxed{9} \]

Answer 2

A reliable check here is to count the opposite side independently and see whether the two counts fit together cleanly. Trace the strip again, this time marking only the red pawns facing away from the blue pawn.

Every red pawn on the strip sits on exactly one of the two sides created by the folds. Tallying the opposite side pawns separately and comparing against the same side group should leave nothing unaccounted for. Retracing the fold pattern from the blue pawn outward still gives 9 red pawns on its side, and the opposite side tally covers the rest, so the count holds up.

the answer is 9