Consider a digital black box with n switches on the front (for some natural numb

Question

Consider a digital black box with n switches on the front (for some natural number n) and an output port that produces some real number output value based on the combination of the settings of each of the individual switches. Each of the switches has three settings, low, medium, and high. By "block box" we mean that the only way to know the output value under some possible combination of switch settings is actually to try out that combination. By "digital black box" we man that the setting of the switches and the reading of the output value can be performed automatically by the computer. Assume that is is essential to find the combination of switch settings that produces the absolutely highest possible output value. If it takes 0.001 second (one one-thousandth of a second) to try out one

Explanation / Answer

a) To determine the highest possible output value we need to check each combination of setting.

Total number of different settings are 3^n.

Therefore, time required to calculate if switches are

5 - 0.243 s

10 - 59.049 s

15 - 14.349 *10^3 s

20 - 3.49 *10^6 s

25 - 8.47 *10^8 s

30 - 2.06 *10^11 s

b) total number of bit evaluations = 3^n *5*n

In the sense of Bremermanns limit 3^n*5*n <10^93

n is approximately 200

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