ATM Puzzle
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A Mysterious Puzzle
To the north, toward Mongolia, is the fierce Gobi Desert. A legendary ATM is said to exist in the Gobi Desert that does not charge any access fees, placed there by the UN during one of its abortive reconstruction plans.
A mysterious Puzzle was found during a visit to this ATM. Eight receipts were found in the ATM, dated on different times on three days; 01/01, 10/10 and 11/01. Each of these receipts were for different accounts, but they all showed the same balance: 34.12Z.
Details
The clues are as follows:
The first receipt is dated 01/01 at 03:06, serving account 0112 3581 3213 4558 9. A balance inquiry follows. 34.12Z in the account.
The second receipt is from 10/10 at 15:28, serving account 1442 3337 7610 987. A balance inquiry follows. 34.12Z in the account.
The third receipt is from 11/01 at 03:15, serving account 1597 2584 4181 6765. A balance inquiry follows. 34.12Z in the account.
The fourth receipt is from 10/10 at 09:11, serving account 1094 6177 1128 657. A balance inquiry follows. 34.12Z in the account.
The fifth receipt is from 11/01 at 15:34, serving account 4636 8750 2512 1393. A balance inquiry follows. 34.12Z in the account.
The sixth receipt is from 01/10 at 03:57, serving account 1964 1831 7811 5142 29. A balance inquiry follows. 34.12Z in the account.
The seventh receipt is from 11/01 at 14:31, serving account 8320 4013 4626 9217 8309. A balance inquiry follows. 34.12Z in the account.
The eighth receipt is from 01/10 at 18:91. Must be an error. The account is 3524 5780 0000 0000 0000. No other information.
The Solution
There are three pieces of critical information in the puzzle; the date, the time, and the account numbers. Arranging the receipts in the order they were found reveals that the dates all correspond to the Golden String:
1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1
The timestamps are slightly altered triangular numbers. (I forgot exactly how I assembled this part. May have screwed up the middle. -- Leo)
The account numbers match the Fibonacci string, but broken up:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 121393 196418 317811 514229 832040 1346269 2178309 3524578
34.12 does not appear to be interesting aside from being repeated. However, in base-7, 3412 is 1234. That was the obscure clue.
Only one of the eight accounts work -- the seventh one. It could be accessed by a 4-digit PIN. This number, discovered by Cinnamon, was 8128.
8128 is a perfect number. It is the 4th perfect number, found by Euclid's formula for perfect numbers. It was the last perfect number known to the Greeks.
for n = 7: 2^6(2^7 − 1) = 8128
The logic of the puzzle involved an understanding of special numerical strings. Once the proper mindset was found, perhaps hinted along by the use of the number "7" (the fourth prime number), or by brute forcing it, the answer became relatively simple to guess.
Why?
Who left this puzzle? What was their objective? Mister Famous claimed not to be involved, so if it was not him, who else? Perhaps more importantly -- were they intending to collect the interest of Strike Force Awesome?
