Countdown to CAT 2020|DAY 116|LRDI
Constraint Based Puzzle
Vikram, an army major, has a safe which contains important documents. The safe can be opened using a six-digit numeric passcode (each digit can be any number from 0 to 9). For security purpose, he changes the passcode every week in the following manner:
i. He adds the first and second digits of his current passcode, the second and third digits, the third and fourth digits, the fourth and fifth digits, the fifth and sixth digits.
ii. The first sum is the first digit of his new passcode, the second sum is the second digit and so on till the fifth sum, which is the fifth digit of his new passcode.
iii. If any of the sums is greater than or equal to 10, he uses only the units digit of the sum in his new passcode.
iv. The sixth digit of his new passcode is the same as the first digit of his current passcode.
1. If the passcode of the safe during a particular week was 786958, what would have been the passcode two weeks earlier?
2. If the first five digits of the passcode during a particular week was 17718, which of the following could have been the passcode two weeks earlier?
3. During two consecutive weeks, Vikram realized that the passcode during the two weeks was the same. Which of the following can be the sum of the first three digits of the passcode?
4. If the last five digits of the passcode during a particular week was 55555, how many possibilities exist for the passcode that he sets the next week?