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# Swapped numbers

## Question

In the ten numerical sequences below, three numbers from each sequence have been moved to another sequence, i.e. 15 numbers have been swapped.

Which 15 pairs of numbers should be exchanged to make each of the sequences follow a regular pattern?

 (A) 37, 85, 148, 232, 333, 442, 589, 744, 917, 1108, 1317, 1544 (B) 42, 84, 144, 219, 310, 417, 537, 679, 834, 1005, 1208, 1395 (C) 44, 95, 166, 253, 368, 493, 650, 821, 1012, 1223, 1454, 1705 (D) 70, 122, 189, 271, 366, 475, 598, 735, 890, 1051, 1230, 1423 (E) 123, 181, 252, 335, 430, 540, 656, 787, 930, 1085, 1283, 1431 (F) 149, 209, 280, 361, 452, 553, 691, 785, 916, 1057, 1192, 1369 (G) 160, 190, 220, 253, 288, 325, 364, 406, 448, 499, 540, 589 (H) 253, 320, 395, 478, 569, 666, 775, 886, 1013, 1144, 1252, 1430 (I) 257, 300, 351, 405, 465, 528, 595, 668, 741, 820, 903, 990 (J) 306, 371, 452, 519, 602, 664, 786, 887, 994, 1107, 1226, 1351

Example

In the two sequences below, 48 and 52 should be swapped to make sense (A5 ↔ B4).

(A) 20, 25, 32, 41, 48, 65. 80

(B) 15, 24, 35, 52, 63, 80, 99

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In each case is there a swap? Or are there longer cycles as well?

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On 10/4/2019 at 2:34 PM, bonanova said:

In each case is there a swap? Or are there longer cycles as well?

On 10/2/2019 at 6:05 PM, rocdocmac said:

In the ten numerical sequences below, three numbers from each sequence have been moved to another sequence, i.e. 15 numbers have been swapped.

Which 15 pairs of numbers should be exchanged to make each of the sequences follow a regular pattern?

 (A) 37, 85, 148, 232, 333, 442, 589, 744, 917, 1108, 1317, 1544 (B) 42, 84, 144, 219, 310, 417, 537, 679, 834, 1005, 1208, 1395 (C) 44, 95, 166, 253, 368, 493, 650, 821, 1012, 1223, 1454, 1705 (D) 70, 122, 189, 271, 366, 475, 598, 735, 890, 1051, 1230, 1423 (E) 123, 181, 252, 335, 430, 540, 656, 787, 930, 1085, 1283, 1431 (F) 149, 209, 280, 361, 452, 553, 691, 785, 916, 1057, 1192, 1369 (G) 160, 190, 220, 253, 288, 325, 364, 406, 448, 499, 540, 589 (H) 253, 320, 395, 478, 569, 666, 775, 886, 1013, 1144, 1252, 1430 (I) 257, 300, 351, 405, 465, 528, 595, 668, 741, 820, 903, 990 (J) 306, 371, 452, 519, 602, 664, 786, 887, 994, 1107, 1226, 1351

Example

In the two sequences below, 48 and 52 should be swapped to make sense (A5 ↔ B4).

(A) 20, 25, 32, 41, 48, 65. 80

(B) 15, 24, 35, 52, 63, 80, 99

I wish to point out a trivial mistake in my OP ...

The value at position C10 (1223) and the one at J11 (1226) have inadvertently not been swapped before posting, So both these values are in their correct placings.

This means that only 14 swaps need to be done.

No extra cycles, all straightforward X Y (one exchange per number with another).

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