The series of resistors in the range 10 Kilohms to 100 Kilohms is: 10k, 12k, 15k, 18k, 22k, 27k, 33k, 39k, 47k, 56k, 68k, 82k, 100k have a tolerance of plus or minus 10%.

(A) You are given a 1.5 Volt cell (battery) and a kit containing one resistor for each of the above values. Using exactly five resistors from the kit, design a circuit which gives the minimum possible, and probably non zero, current in one of the resistors. Draw a sketch of the circuit and explain your design.

(B) Given that each resistor is within plus or minus 10% of its nominal value, what is the range of values that the minimum current of your design could have.

Note: Little electrical knowledge is needed to solve this problem. Only Ohm's Law and Kirchoff's Rules are needed, and these in themselves are pure mathematical rules.

Note to teachers: This question arose from an exercise is designing a math problem around the ten percent resistor series. This question,"Combine Resistors to Achieve Minimum Current" is in the "Math Problem Solving" group at mathematics24x7.ning.com. You are welcome to join, to read more about the background to this question, and to discuss other mathematical problems.

In summary: This question mixes several different concepts, and is difficult to express unambiguously. It is a puzzle, rather than an exercise in algebra. Therefore it fails as a question for assessing mathematical skill. Perhaps it could serve as the basis of an electronics project, one that could be constructed with inexpensive and readily available parts, and that has a non trivial solution.