# The MYSTIQUE sequence

This is the sequence:

0 89 77 175 117 288 222 261
0 83 85 134 190 235 179
0 84 62 181 159 186


Please, write down the next line.

Hint 1:

Also the key is "MYSTIQUE"...

• down the next line. – Keelhaul Mar 26 '18 at 15:02
• @Keelhaul :) :) – Stefano Lonati Mar 26 '18 at 15:24
• do we have to write it with all the numbers? – Kepotx Mar 26 '18 at 15:24
• It seems that $\frac{1}{2}(89 + 77) = 83$ and $\frac{1}{2}(83 + 85) = 84$, so the sequence may start with 0 73 .... The pattern does not generalize to other columns though... – Carl Löndahl Mar 26 '18 at 18:22
• @CarlLöndahl the first two digits are correct but the logic is not exact – Stefano Lonati Mar 27 '18 at 6:27

The next line of the sequence is:

0, 73, 89, 166, 110

The idea here is to add a consecutive pair and divide it by 2, next pair by 3 and then next by 4 and so on. The pattern emerges when you do this with the first and second line, later confirmed by the third line.

A sequence of 83, 84, 73, 81, 85, 69 gives the next line of the sequence order, which in turn is the 2nd number in each line.

The first line is: 0 89 77 175 117 288 222 261

Pattern:

1. (89 + 77)/2 = 83
2. (77 + 175)/3 = 84
3. (175 + 117)/4 = 73
4. (117 + 288)/5 = 81
5. (288 + 222)/6 = 85
6. (222 + 261)/7 = 69

The second line is: 0 83 85 134 190 235 179

Pattern:

1. (83 + 85)/2 = 84
2. (85 + 134)/3 = 73
3. (134 + 190)/4 = 81
4. (190 + 235)/5 = 85
5. (235 + 179)/6 = 69

The third line then confirms it: 0 84 62 181 159 186

Pattern:

1. (84 + 62)/2 = 73
2. (62 + 181)/3 = 81
3. (181 + 159)/4 = 85
4. (159 + 186)/5 = 69

Therefore the fourth line would naturally be following the same pattern as:

Pattern:

1. (73 + x)/2 = 81
2. (x + y)/3 = 85
3. (y + z)/4 = 69

x=89, y=166, z=110

Do tell me how MYSTIQUE is the key here. Couldn't figure that part out.

• +1 for effort and showing us the math. Keep up the good work! – R.D Sep 7 '18 at 4:40