This is my seventh (and probably last) batch of sequence puzzles that are nasty and hard to solve; I stress that each of them has a clear and justifiable solution.
Sequence 1:
RC, NU, RT, RS, PI, ??, AN, PT
Sequence 2:
A, ?, D, ?, G, H, J, K, L
Sequence 3:
?, ?, ?, 1, 7, 0, 7, 1, 7, 3, 4, 8, 9, 3, 4, 1, 2, 4, 2, 5, 9, 1, ?, ?, ...
Sequence 4:
O, ?, ?, H, R, A, U, ?, U, E, ?, ?, ?, ...
Answer
Sequence 1:
TU
These are the third and fourth letters of each planet in the Solar System.
MERCURY, VENUS, EARTH, MARS, JUPITER, SATURN, URANUS, NEPTUNE
RC, NU, RT, RS, PI, TU, AN, PT
Sequence 2:
S, F
These are the keys on the home row of a standard QWERTY keyboard.
A, S, D, F, G, H, J, K, L
Sequence 3:
6, 0, 7, 7, 6
These are the digits in the decimal expansion of e, shifted down by 1.
e = 2.718281828459045235360287...
digits: 6, 0, 7, 1, 7, 0, 7, 1, 7, 3, 4, 8, 9, 3, 4, 1, 2, 4, 2, 5, 9, 1, 7, 6...
Sequence 4:
U, E, O, H, R, A
These are the second letters of each day of the week, cycled around.MONDAY, TUESDAY, WEDNESDAY, THURSDAY, FRIDAY, SATURDAY, SUNDAY
O, U, E, H, R, A, U, O, U, E, H, R, A, ...
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