A 1992-digit number is written. Each two-digit number formed by neighbouring digits is divisible by 17 or 23. The last digit is 1. What is the first digit?
2
Solution was taken from instagram by wesly_ataide:
Two-digit multiples of 17 are 17, 34, 51, 68, 85. Two-digit multiples of 23 are 23, 46, 69, 92. There is only one possible cycle then: 692346. Since it ends with 1, its last digits have to be 692346851. Counting backwards, 2 appears every 5 digits after the 7th, so it's also the 1992nd digit.
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