# Number Sequences Puzzle - Solution

### The Puzzle:

There are infinitely many formulas that will fit any finite series.

Try to guess the next number in each sequence using the simplest mathematical operations or ideas (you may get a different answer than my solution though):

· 8723, 3872, 2387, ?
· 1, 4, 9, 18, 35, ?
· 23, 45, 89, 177, ?
· 7, 5, 8, 4, 9, 3, ?
· 3, 8, 15, 24, 35, ?
· 2, 4, 5, 10, 12, 24, 27, ?
· 1, 3, 4, 7, 11, 18, ?
· 99, 92, 86, 81, 77, ?
· 0, 4, 2, 6, 4, 8, ?
· 1, 2, 6, 24, 120, ?
· 5, 7, 12, 19, 31, 50, ?
· 27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, ?
· 126, 63, 190, 95, 286, 143, 430, 215, 646, 323, 970, ?
· 4, 7, 15, 29, 59, 117, ?
· 4, 4, 341, 6, 4, 4, 6, 6, 4, 4, 6, 10, 4, 4, 14, 6, 4, 4, 6, 6, 4, 4, 6, 22, 4, 4, 9, 6, ?

### Our Solution:

You may have come up with other good and well-reasioned answers, but here are the ones I have:

· 8723, 3872, 2387, => 7238 (moving of numerals)
· 1, 4, 9, 18, 35, => 68 (×2+2, ×2+1, ×2+0, ×2-1, ×2-2)
· 23, 45, 89, 177, => 353 (×2-1)
· 7, 5, 8, 4, 9, 3, => 10, 2 (two series - every second number: 7, 8, 9, 10 and 5, 4, 3, 2)
· 3, 8, 15, 24, 35, => 48 (+5, +7, +9, +11, +13)
· 2, 4, 5, 10, 12, 24, 27, => 54, 58 (×2, +1, ×2, +2, ×2, +3, ×2, +4)
· 1, 3, 4, 7, 11, 18, => 29 (a+b=c, b+c=d, c+d=e)
· 99, 92, 86, 81, 77, => 74 (-7, -6, -5, -4, -3)
· 0, 4, 2, 6, 4, 8, => 6 (+4, -2, +4, -2, +4, -2)
· 1, 2, 6, 24, 120, =>720 (×2, ×3, ×4, ×5, ×6)
· 5, 7, 12, 19, 31, 50, => 81 (a+b=c, b+c=d, c+d=e)
· 27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, => 322, 161 (×3+1, /2, ×3+1, /2 ?)
· 126, 63, 190, 95, 286, 143, 430, 215, 646, 323, 970, => 485, 1456 (/2, ×3+1, /2, ×3+1 ?)
· 4, 7, 15, 29, 59, 117, => 235 (×2-1, ×2+1, ×2-1)
· 4, 4, 341, 6, 4, 4, 6, 6, 4, 4, 6, 10, 4, 4, 14, 6, 4, 4, 6, 6, 4, 4, 6, 22, 4, 4, 9, 6, => 4, 4

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