Understanding the Coding Logic for FROG and DUCK

The problem asks us to find the code for the word 'BEAR' based on the given codes for 'FROG' (92) and 'DUCK' (78). We need to figure out the pattern or logic used to arrive at these numbers.

Let's examine the word 'FROG':

• Find the position of each letter in the alphabet:
  • F is the 6^th letter.
  • R is the 18^th letter.
  • O is the 15^th letter.
  • G is the 7^th letter.
• Sum these positions: \( 6 + 18 + 15 + 7 = 46 \).
• Compare the sum (46) with the given code (92). We can see that \( 46 \times 2 = 92 \).

Now, let's check if this logic holds true for the word 'DUCK':

• Find the position of each letter in the alphabet:
  • D is the 4^th letter.
  • U is the 21^st letter.
  • C is the 3^rd letter.
  • K is the 11^th letter.
• Sum these positions: \( 4 + 21 + 3 + 11 = 39 \).
• Apply the same multiplication factor: \( 39 \times 2 = 78 \).

The sum multiplied by 2 works for both examples. Therefore, the coding logic is: sum the alphabetical positions of the letters in the word and multiply the result by 2.

Calculating the Code for BEAR

Now, we apply this confirmed logic to the word 'BEAR':

• Find the position of each letter in the alphabet:
  • B is the 2^nd letter.
  • E is the 5^th letter.
  • A is the 1^st letter.
  • R is the 18^th letter.
• Sum these positions: \( 2 + 5 + 1 + 18 = 26 \).
• Multiply the sum by 2 according to the logic: \( 26 \times 2 = 52 \).

Conclusion

Following the discovered coding pattern, the code for 'BEAR' is 52.