Posted tagged ‘possibilities’

Spiral Tube Ink Refilling

October 4, 2011

ballpoint pen is a writing instrument with an internal ink reservoir and a sphere for a point. The internal chamber is filled with a viscous ink that is dispensed at its tip during use by the rolling action of a small sphere.


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There are two basic types of ball point pens:

  • Disposable
  • Refillable.

Disposable pens are chiefly made of plastic throughout and discarded when the ink is consumed; Refillable pens are metal and some plastic and tend to be much higher in price. The refill replaces the entire internal ink reservoir and ball point unit rather than actually refilling it with ink, as it takes special high-speed centrifugation to properly fill a ball point reservoir with the viscous ink. The simplest types of ball point pens have a cap to cover the tip when the pen is not in use, while others have a mechanism for retracting the tip. This mechanism is usually controlled by a button at the top and powered by a spring within the pen body, but other possibilities include a pair of buttons, a screw, or a slide.

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Think about it, instead of having a straight tube ink refill, how about fashioning it as a spiral? Agreed it occupies a bit more space so the pen can’t be sleek and slim, but it holds double the amount of ink! There’s a reason why our DNA is structured in a double helix. I guess it will work like a charm for those disposable types, making them last longer.

Daughters’ Ages

August 24, 2011

Two MIT math grads bump into each other at Fairway on the upper west side. They haven’t seen each other in over 20 years.

THE FIRST GRAD SAYS TO THE SECOND: “how have you been?”
SECOND: “great! i got married and i have three daughters now”
FIRST: “really? how old are they?”
SECOND: “well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there..”
FIRST: “right, ok.. oh wait.. hmm, i still don’t know”
SECOND: “oh sorry, the oldest one just started to play the piano”
FIRST: “wonderful! my oldest is the same age!”

problem: how old are the daughters?

Solution

solution: start with what you know. you know there are 3 daughters whose ages multiply to 72. let’s look at the possibilities…

AGES:            SUM OF AGES:
1 1 72            74
1 2 36            39
1 3 24            28
1 4 18            23
1 6 12            19
1 8 9             18
2 2 18            22
2 3 12            17
2 4 9             15
2 6 6             14
3 3 8             14
3 4 6             13

after looking at the building number the man still can’t figure out what their ages are (we’re assuming since he’s an MIT math grad, he can factor 72 and add up the sums), so the building number must be 14, since that is the only sum that has more than one possibility.

finally the man discovers that there is an oldest daughter. that rules out the “2 6 6” possibility since the two oldest would be twins. therefore, the daughters ages must be “3 3 8”.

(caveat: an astute reader pointed out that it IS possible for two siblings to have the same age but not be twins, for instance one is born in january, and the next is conceived right away and delivered in october. next october both siblings will be one year old. if a candidate points this out, extra credit points to him/her.)

this question is pretty neat, although there is certainly a bit of an ahafactor to it. the clues are given in such a way that you think you are missing information (the building number), but whats important isn’t the building number, but the fact that the first man thought that it was enough information, but actually wasn’t.

even if the candidate doesn’t know the solution, they could come up with some interesting thoughts. if they just stare at you and shrug “i dunno” then thank them for their time and don’t give them afogcreek pen.