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Added Value (Posted on 2008-04-13) Difficulty: 2 of 5
Find the next term in each sequence below, replacing the underscores. Then, replace each of the found integers with the corresponding letter of the alphabet (A = 1, B = 2, etc.). The letters, in order, form a five-letter word.

128,  64,  32, 16,  8,  4, ___
 -3,   0,   3,  6,  9, 12, ___
       3,   4,  6,  8, 12, ___
  1,   2,   3,  5,  8, 13, ___
110, 109, 105, 96, 80, 55, ___  

  Submitted by Charlie    
Rating: 2.4286 (7 votes)
Solution: (Hide)
Descending powers of 2:       2 = B
Ascending multiples of 3:    15 = O
Primes plus one:             14 = N
Fibonacci numbers:           21 = U
Subtract successive squares: 19 = S

Of course you could fit a fifth degree polynomial to the shown values in the third row along with any value you'd like for the blank. So if you wanted a 7 there, you could seek a polynomial

ax^5 + bx^4 + cx^3 + dx^2 + ex + f

in which

a + b + c + d + e + f = 3
32a + 16b + 8c + 4d + 2e + f = 4
243a + 81b + 27c + 9d + 3e + f = 6
1024a + 256b + 64c + 16d + 4e + f = 8
3125a + 625b + 125c + 25d + 5e + f = 12
7776a + 1296b + 216c + 36d + 6e + f = 7 (say)

You'd get
-2x^5/15 + 17x^4/8 - 51x^3/4 + 287x^2/8 - 2707x/60 + 23

This was designed to, and does, provide the next term (x=6) of 7. But that would be BOGUS. To get true Extra Value, you need a BONUS.

From Page-a-Day, 2008 Mensa 365 Brain Puzzlers calendar.
(called that, even though it has a leap-year-day puzzle.)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
No Subjected bottemiller2008-04-14 16:18:22
Value of Problem - re Ay and Dej Mar.brianjn2008-04-14 06:01:17
SolutionSolutionDej Mar2008-04-14 02:50:56
No Subjectbucks2008-04-14 02:00:06
SolutionNo SubjectAdy TZIDON2008-04-14 01:38:40
No SubjectAdy TZIDON2008-04-14 01:35:53
SolutionSolution?Steve Herman2008-04-13 12:16:03
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