Permutations & Combinations
ATM Pin with Constraints
nta_pyq_2023_apr
Grade 11
Question:
A 4-digit PIN: all digits different, greatest digit $=7$, sum of first two $=$ sum of last two. Maximum trials needed is ________.
Step-by-Step Solution
Key Concept: Digits all different, max digit $=7$, so digits from $\{0,\ldots,7\}$ with 7 included. $d_1+d_2=d_3+d_4$. Count valid PINs.
72 trials.
Correct Answer: 72