When I first saw that problem, the first thing I did was calculate the circumference of the Earth in feet (~25,000 miles x 5280 = 132,000,000 feet), then divide 1 by the circumference to get 0.000000008 feet (rounded, about 2.3 nanometers), or in other words, impossible with any realistic knife. Upon reading further replies, including yours, I tried it out myself with a tape measure on various circular objects and found that it was indeed possible. Just hard to imagine that such a small relative change could cause such a large gap when distributed over the entire Earth.
Regardless of whether it is an exam, a recipe, or a programming language that involves numbered lines of code, reading the whole thing before you start does not override the convention that numbered steps or questions are executed in number order.
Upon first reading of the problem, I thought it is not possible. Then I tried algebra. It is interesting to note that C1 & C2 cancels out. That means this will hold true for any sphere, where circumference is increased by 1 foot.
The problem is that you had calculated an irrelevant quantity. The ratio of added circumferential length : existing circumferential length (1 foot : circumference of Earth) has nothing to do with whether you can slip a knife under; the fact that 0.000000008 feet is very small is of no relevance.
Slipping a knife under is a question of the added radius, not the percentage increase in circumference. And as we all know, radius is proportional to circumference, so adding 1 foot to circumference adds 1 foot/(2π) to radius, no matter how big or small the existing circumference is in comparison to 1 foot.
Also, keeping track of units, the ratio 1 foot : circumference of Earth is a dimensionless 0.000000008, not 0.000000008 feet. Which also shows it to be irrelevant; you can’t compare the width of a knife to a dimensionless value.
Both dimensions are expressed in " foot". When you divide 2 quantities, where both are expressed in foot, the result will be just a number without a dimension.
