Xref: utzoo rec.puzzles:2269 sci.electronics:4355 Path: utzoo!utgpu!watmath!watcgl!awpaeth From: awpaeth@watcgl.waterloo.edu (Alan Wm Paeth) Newsgroups: rec.puzzles,sci.electronics Subject: Re: Resistor Puzzle Message-ID: <7079@watcgl.waterloo.edu> Date: 1 Dec 88 18:32:07 GMT References: <6951@watcgl.waterloo.edu> Reply-To: awpaeth@watcgl.waterloo.edu (Alan Wm Paeth) Distribution: rec Organization: U. of Waterloo, Ontario Lines: 23 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