Two rules, two patterns, step by step

Two rules run side by side: add 3 along the top, add 9 along the bottom.

The question

Two rules, two patterns

row 1:530
row 2:1060
row 3:1590
row 4:20?
row 1:530
row 2:1060
row 3:1590
row 4:20?
row 1:530
row 2:1060
row 3:1590
row 4:20?
row 1:530
row 2:1060
row 3:1590
row 4:20120
  1. Two patterns, and each column counts in its own step — so a gap CAN be filled by counting down its own column. But that is not what a table of pairs is for: the two sides are locked to each other, and the same link works on every row.
  2. Read the link off a row with nothing missing. Row 1: 5 on the left, 30 on the right — that is × 6.
  3. The same link holds all the way down, so use it on the gap: 20 × 6 = 120.
  4. Counting down the column gets there too — this is not a trick — but the link is what the two patterns were put next to each other to show.

How it works.

  1. 01

    Two patterns, and each column counts in its own step — so a gap CAN be filled by counting down its own column. But that is not what a table of pairs is for: the two sides are locked to each other, and the same link works on every row.

  2. 02

    Read the link off a row with nothing missing. Row 1: 5 on the left, 30 on the right — that is × 6.

  3. 03

    The same link holds all the way down, so use it on the gap: 20 × 6 = 120.

  4. 04

    Counting down the column gets there too — this is not a trick — but the link is what the two patterns were put next to each other to show.