## Posted tagged ‘side’

### 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.

### SMART GLASS WITH SPD TECH

August 22, 2011

Electro-chromatic mirrors system:

Electro chromatic mirrors / Auto dimming mirrors use a combination of opto electronic sensors and complex electronics (sensors, circuit boards, micro-controllers, etc.) that constantly monitor ambient light and the intensity of light shining directly on the mirror. As soon as sensors detect glare, the electro chromatic surface of the mirror becomes darker to protect driver’s eyes and their concentration.

The electro chromatic technology usually is applied to the inside rearview mirror / Side view mirror, where it basically saves you the trouble of flipping the mirror manually if blinded by the light which increases driving safety.

Working operation of Electro chromatic mirrors:

This auto dimming rearview mirror is installed on higher end vehicles. It consists of two lenses that sandwich an electro chromic (electronic color changing) gel. The inside sides of the lenses are coated with a transparent conductive layer coating and the deepest lens has a reflective coating.

This gel, when charged with electricity darkens, then clear once the glare is no longer detected. The mirror uses a forward sensor which measures the outside ambient light, and a rearward sensor to look for glare. When dark enough, it sends current to the electrostatic gel, darkening it a rate which is related to the level of ambient darkness and rearward glare. When the outside ambient light increases, the current decreases, until the gel is clear again at daylight light levels.

Electro chromatic auto dimming rear view mirror