20:40, the armchair, a borrowed book
A rule does not need a mark at every centimetre, only enough marks that every length lies between two of them. With marks at 0, 1, 6, 9, 11 and 13 nothing is missing: 7 is from 6 to 13, 10 is from 1 to 11. Six marks make fifteen pairs and thirteen lengths are wanted, so two pairs are spare: there are two ways to measure 2, and two to measure 5. Thirteen is the most that six marks can do, and five marks stop at nine: John Leech studied the problem in 1956, and the small cases are settled by trying every arrangement, which finds three such rules and their mirror images. A rule with nothing to spare, every length exactly once, exists only up to four marks, at 0, 1, 4 and 6; beyond that one settles for no length twice, which is a Golomb ruler, and a way of spacing the antennas of a radio telescope.
Objects · Pocket rule in brass, also a bookmark
Four Notches
CHF 34 working price
For the page you were on, and for any whole number of centimetres up to thirteen.
A strip of brass 13 cm long that keeps your place in a book and measures any whole number of centimetres from 1 to 13. It has six marks only, its two ends and four notches: find the pair the right distance apart.
A study: nothing can be ordered yet. The photograph is a generated image, not a picture of a made piece or of a real person.
- Half-hard brass strip, 130 × 20 × 0.6 mm, about 13 g: thin enough to stay in a closed book, stiff enough to rule a line; square ends, corners just broken
- Four V notches 2 mm deep on one long edge, at 10, 60, 90 and 110 mm from one end, placed within 0.05 mm: with the two ends, six marks. A pencil point sits in a notch
- The other long edge is plain: a straightedge. No numerals, no scale, nothing printed or engraved, nothing red
- In a sleeve of the notebook’s slate book cloth; a number stamped small on the back
