A certain computer scientist has designed a remarkable machine which gives a correct answer to any yes no question typed into it via its keyboard. The machine answers by flashing a blue or a yellow light, one of the colors signifing "yes", the other "no". The machines come with no instructions nor are the lights labeled. Worse, a given machine in stores now has equal probability of having been manufactured in either China or Malaysia, and it is known that the two different countries have selected opposite conventions for which color means yes, but it is not at present known which country signified yes by blue, and which signified yes by yellow. You have just unpacked a machine, plugged it in, and turned it on. Each of the choices below is a separate question. In other words, in answering (d), assume you have not tried any of the questions appropriate for (a), (b), (c) - in other words, assume in each case you are going to ask only one specific question, and have asked no questions previously. (a) What one yes/no question could you ask the machine which would allow you to determine whether it was made in China or Malaysia? (b) Suppose instead of wanting to know which country your specific machine was manufactured in, you just want to know whether it was the Chinese or Malaysian machine that means "yes" by blue. What single yes/no question could you ask your machine to determine this? (c) Suppose all you want to know is, for your specific machine, which color means "yes" and which color means "no" (d) What yes/no question is such that the machine, no matter what country it is manufactured in, is bound to answer by flashing yellow?
5 years ago