Sunday, May 11, 2014

TWO HOURGLASSES to measure 2 minutes

Problem

You have two sand hourglasses, one that measures exactly 4 minutes and one that measures exactly 7 minutes. You need to measure out exactly 2 minutes to boil an egg. Using only these two hourglasses, how can you measure out exactly 2 minutes to boil your egg? 
What if boiling eggs  take 9 minutes?
 

Solution

Boiling the eggs take 2 minutes
4 minutes : 7 minutes
#1:#2
4 : 7 Start both timers
0 : 3 After 4 min
4 : 3 Invert #1
1 : 0 After 3 min
1 : 7 Invert #2 and start cooking egg
0 : 6 After 1 min (egg half-cooked)
0 : 1 Invert #2 (7-6 = 1)
0 : 0 Stop cooking egg.
 
Total time from start: 7 min  

Boiling the egg taking 9 minutes
4 minutes : 7 minutes
#1:#2
4 : 7 Start both timers
0 : 3 After 4 min
4 : 3 Invert #1
1 : 0 After 3 min...#1 has 1 minute remaining
1 : 0  Leave #2 and start cooking egg
4 : 0 Invert #1. After 1 min (egg is 1 min-cooked)
0 : 0 Invert #1
4 : 0 Stop cooking egg.
 
1+4+4 = 9 minutes
 

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