Lines and arrows
This page covers rules drawn along a path of cells: lines (6.4) and arrows (6.5).
6.4 line
{"type": "line", "kind": "thermo", "cells": ["r5c3", "r4c3", "r3c3", "r3c4"]}
{"type": "line", "kind": "whisper", "value": 5, "cells": ["r7c7", "r7c8", "r8c8"]}
{"type": "line", "kind": "renban", "closed": true, "cells": ["r2c2", "r2c3", "r3c3", "r3c2"]}
Common fields: cells (ordered, at least 2) and closed (default false): a loop, the last cell connects back to the
first. closed is allowed only for whisper, renban and parity.
kind | Parameters | Meaning | Drawing |
|---|---|---|---|
thermo | – | Strictly increasing from cells[0] (the bulb). Branching thermos are separate rules sharing cells[0]. | |
slow_thermo | – | Non-decreasing from cells[0]. | |
whisper | value k (1..D−1): REQUIRED when D ≠ 9; default 5 | Adjacent cells on the line differ by at least k (German whisper = 5, Dutch = 4). | |
renban | – | The cells hold a set of consecutive digits, no repeats, any order. | |
region_sum | – | Split the line into segments wherever it passes from one box to another; every segment has the same sum. Boxes are those of box_grid and box rules (jigsaw pieces included); extra regions, windows and diagonals do not split the line. | |
palindrome | – | Reads the same from both ends. | |
entropic | groups: REQUIRED when D ≠ 9; default [[1,2,3],[4,5,6],[7,8,9]] | Every run of 3 consecutive cells holds one digit from each group. | |
modular | value m (≥ 2): REQUIRED when D ≠ 9; default 3 | Every run of m consecutive cells holds one digit of each residue class mod m. | |
parity | – | Adjacent cells on the line differ in parity (alternate odd / even). | |
zipper | – | Cells equally far from the centre of the line sum to the same total (the centre digit, for an odd length). | |
between | – | Digits strictly between those of the two ends cells[0] and cells[-1], ends in either order. | |
lockout | value k (1..D−1): REQUIRED when D ≠ 9; default 4 | The ends differ by at least k; every other digit lies outside the closed range of the ends. | |
double_arrow | – | The two ends sum to the total of the cells between them. |
Repeats: allowed on every line (subject to houses), except renban.
6.5 arrow
{"type": "arrow", "bulb": ["r2c2"], "lines": [["r3c3", "r4c4", "r5c5"]]}
{"type": "arrow", "bulb": ["r1c1", "r1c2"], "lines": [["r2c3", "r3c3"], ["r2c1", "r3c1", "r4c1"]]}
bulb: 1 or more orthogonally connected cells, read as one number inbulborder (a pill [a, b] is 10·a + b).lines: 1 or more shafts, each ordered away from the bulb; the first cell of each shaft touches a bulb cell.- Each shaft's digits sum to the bulb number. Repeats allowed.