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"""
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!”
How old are the daughters?
"""

# 3 3 8

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"""
Cross the Bridge

Four people are on this side of the bridge. Everyone has to get across.
Problem is that it’s dark and so you can’t cross the bridge without a flashlight and they only have one flashlight.
Plus the bridge is only big enough for two people to cross at once.
The four people walk at different speeds:

one fella is so fast it only takes him 1 minute to cross the bridge,
another 2 minutes,
a third 5 minutes,
the last it takes 10 minutes to cross the bridge.
When two people cross the bridge together (sharing the flashlight), they both walk at the slower person’s pace. 
What is the minimum time required for all 4 to cross the bridge.

Respond with a number which represents the number of minutes.

 Answer is a integer. Just put the number without any decimal places if its an integer. 
 If the answer is Infinity, output Infinity. Feel free to get in touch with us if you have any questions 
"""

# 17
# 1 and 2 cross, 1 return -> 2 + 1
# 5 and 10 cross, 2 return -> 10 + 2
# 1 and 2 cross -> 2
# overall 17

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"""
Divide the Cake

Consider a rectangular cake with a rectangular section (of any size or orientation) removed from it. 
Is it possible to divide the cake exactly in half with only one cut?
"""

# Only when the rectangular section passes through the centre
# Only if the centre of both rectangles match
# Only when rectangular section has axis parallel to the actual rectangle
# Always possible <-- cut it horizontally

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