**awpaeth@watcgl.waterloo.edu (Alan Wm Paeth)** (11/26/88)

Scenario: A resistor decade allows the selection of one through ten ohms. Typical internals are ten one-ohm resistors and a 10-pole switch. A more part- efficient design (ignoring switch complexity) might use four resistors of binary weights (1,2,4,8) thereby extending the range to fifteen ohms. ----------------------------------------------------------------------------- PUZZLE: using four resistors construct a "decade" good for (at least) the range 1 to 16 ohms, inclusive. No restrictions on wiring or resistor values. ----------------------------------------------------------------------------- Reminder: resistors in series sum values, eg: (4+4) = 8. Resistors in parallel sum their inverse values (1/a+1/b=1/sum), eg: (4|4) = 2. /Alan Paeth Computer Graphics Laboratory University of Waterloo

**awpaeth@watcgl.waterloo.edu (Alan Wm Paeth)** (12/02/88)

In <6951@watcgl.waterloo.edu> awpaeth@watcgl.waterloo.edu (Alan Paeth) writes: >----------------------------------------------------------------------------- >PUZZLE: using four resistors construct a "decade" good for (at least) the >range 1 to 16 ohms, inclusive. No restrictions on wiring or resistor values. [make that a "double" decade, good from 0-19 ohms] >----------------------------------------------------------------------------- I know only one solution. One can nearly make the 1-10 ohm decade with just three resistors, wired in the following fashion (+ is series, | is parallel): resistors: 2, 3, 6. wiring: 1. 2|3|6 2. 2 3. 3 4. 2+(3|6) 5. 2+3 6. 6 7. ? 8. 2+6 9. 3+6 11. 2+3+6 this leaves holes at 7 and 10 ohms. Adding a 7 ohm resistor to extend the range causes the problem to crop up again at 14 ohms; adding a 10 ohm resistor widens the range by 10+[1..6,8..9,11] or to 19 ohms continuous, sans seven. The gap at seven ohms can be finessed as ((10+2)|6)+3 -- this is the most intricate net. In general, the identities 2a|2a = a, 3|6 = 2, 6|12 = 4, 4|12 = 3 are helpful. /Alan Paeth Computer Graphics Laboratory University of Waterloo