Example 1 12|16|20[10] 22 Example 2 1|3|5[2 1/2] 3 1/2 Example 3 30|40|50[15] 65 Can you use the examples to find x? 12|16|x[0] 32
Find the pattern isn't math. Absent a model, there are always an infinite number of ways to predict a missing value. For this sequence a|b|c[r]s we have the following seemingly significant relationships: 2b = a + c = r + s b - a = c - b which are consistent with x = 20 And we have (2r -a)(2r - c) = 0 which is consistent with x = 0. But the same evidence for (2r -a)(2r - c) = 0 also supports (2r -a)(2r - c)(r) = 0 which is consistent with x = 20 . And we have (2s - 2b - c)(2s - 4b + c) = 0 which is consistent with x = 32. But the same evidence for (2s - 2b - c)(2s - 4b + c) = 0 also supports (2s - 2b - c)(2s - 4b + c)(2s - 4b) = 0 which is consistent with x = 20 . This hypothesis equivalent to a claim the pattern has 3 degrees of freedom (o, p, q) a = p + q b = 2p + q c = 3p + q r = p - o s = 3 p + 2 q + o p : q : o : a | b | c [ r ] s 4 : 8 : -6 : 12 | 16 | 20 [ 10 ] 22 2 : -1 : -1/2 : 1 : 3 : 5 [ 5/2 ] 7/2 10 : 20 : -5 : 30 : 40 : 50 [ 15 ] 65 4 : 8 : 4 : 12 | 16 | 20 [ 0 ] 32 A useful puzzle would either give more examples or have less degrees of freedom. Finally -- it was entirely unnecessary to start a new thread for this.
