## Jeremy’s Convoluted Calculus

Jeremy, one of our favorite students, has provided another problem for us! This time it’s a word problem that has its’ origins in the ninth century, and was a personal favorite of Lewis Carroll. This week’s problem would seem to be easier than last week’s teaser…or is it?

Once upon a time a farmer went to market and purchased a fox, a goose, and a bag of beans. On his way home, the farmer came to the bank of a river and hired a boat. But in crossing the river by boat, the farmer could carry only himself and a single one of his purchases – the fox, the goose, or the bag of the beans.

If left alone, the fox would eat the goose, and the goose would eat the beans.

The farmer’s challenge was to carry himself and his purchases to the far bank of the river, leaving each purchase intact. How did he do it?

The first person to solve the problem will get a \$50 gift certificate towards private tutoring or a prep class, along with a very nice Chyten water bottle.

## Jeremy’s Convoluted Calculus

One of our genius-level mathematics students delights in taunting the staff with difficult upper-level math problems (which he writes on the board in one of our private tutoring rooms). The one that he provided us with this week is particularly maddening, and so we’ve decided to solicit some answers from the outside. This week’s conundrum?

I’ll denote a repeating decimal by .[abc]
Convert this decimal to fractional form and simplify: .[1273]
In addition, prove why 1/3 = .[3] using the same method you used to figure out the previous

The first person to solve the problem will get a \$50 gift certificate towards private tutoring or a prep class, along with a very nice Chyten water bottle.