It’s pure adrenalin rush when you see John McClane running around in narrow by-lanes trying to crack various riddles/puzzles so as to prevent a psycho terrorist from blowing up New York city. Ofcourse I am referring to the ‘ Die Hard’ movie with Bruce Willis playing the smart cop John McClane. I can watch this movie anytime any number of time – not so much because of its hero or the action quotient but more so because of the intricate interweaving of the plot with the puzzles/riddles which seems to have added that extra zing in an otherwise typical masala flick. Puzzles have fascinated me for all of my life and I regret that there is no daily hardcore ‘puzzle’ column in daily newspapers just as they have for crossword section. I have seen some of the smartest puzzles which I could never crack and then had to rely on other sources/ more intellectual friends for getting the solution. Many often than not, it’s the unique framing of the puzzle which adds the ‘grey’ quotient to the whole conundrum than the solution itself. Words play an extremely significant role here and a slight slip of tongue can spoil the entire puzzle. A simple example that comes to my mind – A boy along with his father meets with a car accident and while the boy survives, his father dies on the spot. When the boy is brought to the hospital, the doctor upon seeing the boy exclaims – ‘He is my son’ – how is that possible?? Now I really have to confess here I couldn't crack this puzzle. The answer is so simple and I kept thinking all the various angles including some supernatural angles (a la ghost theories etc) to explain the riddle. But if you analyze the framing of the puzzle carefully, no where its mentioned or hinted that the doctor was a ‘female’ doc which makes the puzzle so simple to guess.
Alright so this blog is about one specific puzzle which I came across recently. This brainteaser is a simple, run of the mill arithmetic puzzle and I do enjoy cracking the underlying logic for such puzzles. So here it is as mentioned below –
If
8 + 8 + 8 = 6
6 + 6 + 6 = 3
1 + 1 + 1 = 0
3 + 3 + 3 = 3
4 + 4 + 4 = 3
What is 1 + 2 + 9?
What is 9 + 9 + 9?
What is 0 + 0 + 0?
My solution was as below –
1) Divide each of the number by 4
2) Rounds off any fraction to nearest whole number (keeping in mind ceiling/floor concept, .50 to be rounded off to its ceiling number)
3) So with above logic, the answer comes out to be –
What is 1 + 2 + 9? = 2
What is 9 + 9 + 9? = 6
What is 0 + 0 + 0? = 0
So far so good. Now I have a good friend Supriya who likes to play around with puzzles a lot and I always share any good puzzle with her (especially if am unable to crack it as she is really good in cracking them anyhow). She replied back with same answers and I beamed with a smile as she too had corroborated my solution. But then things took a dramatic turn – when I asked her if she had used the same logic as I did (providing details as per above solution), she replied back in negative. I was absolutely intrigued – as I know there can be more than 1 solution to any given problem but not 2 approaches to same solution. Her solution was based on arithmetic progression as per below –
1) First 2 numbers in natural numbers are assumed to be zero – so 1 and 2 both are equal to zero (1,2=0)
2) Next 3 numbers are assumed to be 1 – so (3,4,5= 1)
3) Next 4 numbers are assumed to be 2 – so (6,7,8,9=2)
4) So with above logic, the answer comes out to be same as mine –
What is 1 + 2 + 9? = 2
What is 9 + 9 + 9? = 6
What is 0 + 0 + 0? = 0
I was really puzzled with the puzzle co-incidence here. It was a first for me that 2 different approaches produced same results. May be this is a freak co-incidence but still for me, this is a classic example of serendipity!
