Question

A device classifies numbers according to the following criteria. The number must have: (A) Five digits (B) First and last digits are perfect squares. (C) The middle digit is an odd number and it is an addition of first and last digits. (D) Second and fourth digits are the difference between first and third digits, third and fifth digits.

Which of the following numbers could be correct according to the conditions given above?

Accepted Answer

A. Let the 5-digit number be $d_1 d_2 d_3 d_4 d_5$. Let's test option **14514**: - Condition A: 5 digits (Yes) - Condition B: $d_1 = 1$ (perfect square), $d_5 = 4$ (perfect square). (Yes) - Condition C: Middle digit $d_3 = d_1 + d_5 = 1 + 4 = 5$, which is an odd number. (Yes) - Condition D: - Second digit $d_2 = |d_3 - d_1| = |5 - 1| = 4$. - Fourth digit $d_4 = |d_3 - d_5| = |5 - 4| = 1$. - So $d_2 = 4$ and $d_4 = 1$, matching 14514! (Yes) Hence, 14514 satisfies all criteria.

Five Digit Code Criteria

Explanation

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