Executive talent is hard to come by, and it is not cheap. Folks at the water cooler have no ideas, and the coffee-breakers can't imagine how to improve things either. But those who party around the teapot, they came up with something. They suggested to the Board that Acme promote the newest hire in the mail room and make him the CEO! We need to shake things up, but good. Qualifications, job experience, brains, judgment, integrity, these are all things of the past.

Some were not so sure. Doesn't make sense at all, the old timers said. Almost like appointing some guy with orange complexion to be President. That's exactly the idea, said the tea-people. Turn things on end, let the bull loose in the china shop, and see what happens. Hey -- how could it be worse than what we have now? Not surprisingly, the debate was long and heated.

Such a risk merited proof of possible gain, so the old guard posed a challenge: produce a concrete example of where the idea had been tried with incontrovertible benefit. In fact, make it mathematical. You know, something that might make a good BrainDen puzzle.

We'll promote the mail room guy, they said, if you can show us an integer that doubles in value when its least significant digit is promoted to its most-significant position.

That is, give us a number { some digits } q that has half the value of q { same digits }.

Spoiler

102 doesn't quite work, since 210 does not quite equal 204

That all happened last week, and now we're looking for the mail room guy. Was he promoted? Did the tea people find such a number? Is there one?

We need a number or a proof that one does not exist.

T.L.D.R.

What number doubles in value by by moving its last digit to the first position (if there is one)?

Things are not going well at the Acme Company.

Executive talent is hard to come by, and it is not cheap. Folks at the water cooler have no ideas, and the coffee-breakers can't imagine how to improve things either. But those who party around the teapot, they came up with something. They suggested to the Board that Acme

promote the newest hire in the mail room and m! We need to shake things up, but good. Qualifications, job experience, brains, judgment, integrity, these are all things of the past.ake him the CEOSome were not so sure. Doesn't make sense at all, the old timers said. Almost like appointing some guy with orange complexion to be President. That's exactly the idea, said the tea-people. Turn things on end, let the bull loose in the china shop, and see what happens. Hey -- how could it be worse than what we have now? Not surprisingly, the debate was long and heated.

Such a risk merited proof of possible gain, so the old guard posed a challenge: produce a concrete example of where the idea had been tried with incontrovertible benefit. In fact, make it mathematical. You know, something that might make a good BrainDen puzzle.

, they said, if you can show us an integer that doubles in value when itsWe'll promote the mail room guyis promoted to itsleast significant digit.most-significant positionThat is, give us a number { some digits }

that has half the value ofq{ same digits }.q102 doesn't quite work, since 210 does not quite equal 204

That all happened last week, and now we're looking for the mail room guy. Was he promoted? Did the tea people find such a number? Is there one?

We need a number or a proof that one does not exist.

T.L.D.R.What number doubles in value by by moving its last digit to the first position (if there is one)?

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