Question

A girl counts fingers: 1 = thumb, 2 = index, ..., 5 = little finger, then reverses. Count reaches 1994. Which finger does she end on?

• A. thumb
• B. index finger
• C. middle finger
• D. ring finger

Hint:

When pattern is cyclic, use modulo to find position in the repeating sequence.

Answer 1

The Correct Option is B

Finger sequence: \[ 1 \to 2 \to 3 \to 4 \to 5 \to 4 \to 3 \to 2 \to 1 \to 2 \to \dots \] This forms a cycle of 8 steps: \[ 1 \to 2 \to 3 \to 4 \to 5 \to 4 \to 3 \to 2 \text{length = 8} \] So, it repeats every 8 counts. We want to find finger at count 1994. \[ 1994 \mod 8 = 1994 - 8 \times 249 = 1994 - 1992 = 2 \] So 2nd finger in the cycle = \boxed{index finger}