An ode to Bruno

For those of you who are wondering who Bruno is, he is ( technically was ) my pet dog. He is such a darling. He is the long hair dog types, with a nice, small, forever wet nose. His hair had a tinge of brown and hence the name Bruno. So cute. So pretty. So stylish.

You know, one day, when he was young, my dad was carrying him and walking towards the car.. and one neighbour's kid excitedly tugged on his amma's saree and exclaimed, ( out loud ), "Amma, lion lion lion." My dad couldn't hide the smile escaping out of his pride exuding face...

Bruno was actually a birthday gift for my dad, years back. My mom went to pick him from the pet store, and apparently, he was the quietest puppy in the store. She said, "He seemed unperturbed by the fact that there were visitors in the shop. So, he must be the nice, cuddly types and quiet types." She sure was in for a big surprise!!

The day he came home, exactly a day before my dad's bday, was what we celebrated as his birthday all these years. Over the years, he even learnt to wag his tail as soon as we sprang a " happy birthday to you , happy birthday to Bruno" on him.  My brother decked him up with gogs and a cap on his birthday and he loved it. 

It so happened that I wasn't present when Bruno was brought home. I still remember my dad used to say that he resembled a small tennis ball. So small. And after a week to settle, he started walking slowly.. and he looked like a toy dog that could be keyed to move. Some said they had mistaken him for stuff toy, and were totally surprised when it moved towards them. ( he was too small to bark at visitors back then ) and back then our house used to be filled with small circles of his pee here and there. And mom used to follow him everywhere and clean up immediately ( owing to her obsessive compulsive disorder for cleanliness )

So I was in a hostel when he was brought home. And when I came for my holidays, he was already 6 months old. And just the opposite of what my mom thought him to be. Very naughty and an extremely alert watch dog who wouldn't let anyone enter. His first sworn enemy was our maid who paid a visit to our house from 9-12.  And at that time it looked like his second enemy was me. He didn't know me at all, so he treated me like an outsider. I was greeted by ferocious barks when I came home for my break. I was scared. Then my dad took him aside ( you've got to believe this...  ) and spoke to him and said ," She is my daughter. My family. Our family. You have to stop barking at her." And he brought him closer to me.. I was so scared that I wud've (undoubtedly) been the reason for another puddle in my house !! But to my surprise, Bruno sniffed my hand and then wagged his tail and let me go. However, just to be sure, for one whole week, he followed me everywhere , and I heard a growl every time I got near the music system, or went to the kitchen to get a plate. I was shattered. I went to my dad and said ," This is my house. He cannot treat me like that". My dad smiled and said ," Give him a chance dear. He is just doing his duty." I still remember rolling my eyes at that comment. Oh, what a long way we've come after that!!

So much so that, when I was preggy, I practised carrying a baby by carrying him.. I have a photo to remember that thought, u know! 

My mom toilet trained him, taught him the native language. She spoke to him like she spoke to anyone else, and he understood it all. So much so that my mom and dad used to spell words out when they didn't want him to understand. Any parent of a toddler would relate to that completely. He was never treated as a pet, leave alone dog. He was a member of our family.  He considered my bro as his bro/friend, ( owing to the fact that I was never at home )  and there was so much of sibling rivalry between them. (You would see them fighting for who gets to lie down next to my mom.)  You should see both of them run around and play too.. they were best buddies. 

Cooked chicken and rice was his staple diet. No pedigree. Nothing else. Morning walk for morning duties, barking at the slightest noise he could hear, ( loud playing kids, newspaper wala, milk man, security, maid, any vehicle that went by) and following my dad everywhere he went inside the house.. were his daily routine/duties. He could actually sense my dad's car from way beyond the street... when we see him wag his tail non stop for like 5 mins, standing near the door, we would know my dad is almost here.

After my son was born, again, the Bruno who didn't like kids, the Bruno who hated anyone apart from us, invited my son with open arms. I still wonder how he knew, how he understood. And we call them 5 sensed!! He was utterly loyal to us, kept awake and vigil in the night, was always eagerly at the window waiting for us to come back when we stepped out for daily errands. How could anyone love anyone so much. 

All of us loved him, he loved us. We took so much care of him. He left us on the 17th of this month, and we are all devastated. He was so much a part of our lives that the house suddenly felt empty. I live away from home now and when my mom called me and informed me that he passed away, it felt like my heart was getting sucked into a black hole. I came home and all I could see was a mound of earth. Our lovely dog, our friend, our lovable companion was no more. He left a permanent hole in our hearts. It's still not settling in you know, why do dogs get to live so less ?? My son believes that Bruno would return as a crow ( it is common in our culture to believe that the ancestors come back as crows to see us). He wiped my mother's tears and tells her ,"Ammachi, don't worry, I will pray and meditate to lord Brahma and when He appears before me and grants me a boon, I will ask God to wake Bruno up". My mom pulls him closer and hugs him tight, with tears streaming from her eyes. If only that could happen !! Sigh. Sad sigh!! May his soul rest in peace. We love you Bruno!

Magic triangle

What is this magic triangle.. what could it be . Let me break the suspense, this is a number puzzle. Like every triangle, this one also has three sides. Each of its sides contains equal amount of some numbers. ( numbers that do not repeat itself. In our case, we want it to be from a set of consecutive numbers )  And the sum of the numbers placed on each side turn out to be the same.

That is, like this : Arrange numbers from 1-9 on a magic triangle of size 4, such that each side adds up to the same number. Now, this is not that difficult. If not anything, we could always try a trial and error after ruling out some obviously impossible combinations. ( like the big numbers 8,9 don't end up on the same side) 

Take a break and try arranging the numbers so that they add up to 17 on each side. Try it!! 

That's great.. now, what if I asked you to arrange numbers from 1-15 in a magic triangle of side length 6. Now what would you do? Would be real crazy and time consuming to try out combinations for those many numbers. What to do...  what do we usually do... the first approach to trying to come up with an algorithm that will help us work out triangles of any length, would be , to start off with smallest case. Triangle of size 3, then try triangle of size 4. Then see if we could generalise it. Again, take sometime if you feel like giving it a try. I can wait. 

This is the algorithm I found useful and pray that it works for laarge numbers too..  Time to visualise our triangle. Imagine a triangle with three vertices named as A, B and C. ( The side BC is the horizontal side , the AB is the left side and AC is the right side )

You are given a series of consecutive numbers to fit into the triangle along its sides equally so that the sum of each individual side is the same . 

Start with the vertex A. That is, the first number of the series, place it on A. The next number on B and the third number on C. Now, remember this rule : every number thereafter follows a pattern, wherein , each side gets a turn, that is, each side gets a number and waits two turns to get the next number. ( that is no two consecutive numbers go to the same side . You will understand this better with an example. ) 

While distributing the numbers now, say n, n+1, and n+2 ( three consecutive numbers ) , we already said, each side gets one. But which side should get which number is the thing to concentrate on. Out of the three numbers, the middle number always goes to the side BC( the horizontal side ) . The first number goes to the right side in the first iteration, and in the second iteration the first number goes to the left side (alternatively that is).

To apply all this confusing data on an example : Vertex A gets 1, B gets 2 and C gets 3. Number 4 goes to the right side, 5 to the horizontal side, 6 to the left side. Now iteration 2, number 7 goes to left side first, 8 ( middle number ) goes to horizontal side and 9 goes to the right side now. You see , 1,2,3 sat on the vertices. 4,5,6 -  start from  right side, middle in horizontal side, 6 on the left side. next iteration : 7,8,9 ( this time, we start from left side ) left gets 7, horizontal gets 8 and right gets 9. 

We do this till we reach the last iteration. The last three numbers : till now we were trying to balance the sides so that they all had more or less similar sum, last turn we make the sum equal. The last iteration, say x, x+1, x+2. Again, each side gets one number each.  For the last iteration, the first number x goes to the horizontal base. But where x+1 goes depends on which side's turn it is. ( if in the previous iteration, the left side got the first number in the series, this turn the right side gets the second number. In simpler terms, if it's an odd iteration, pick the right side, and for an even iteration pick the left side. ) Ta daa.. there comes our magic triangle.

Quick recap : First three numbers on vertices in anti clockwise order. The next three number follow a pattern: middle number always on BC. Where the first number goes depends on the iteration number. First iteration, first number goes to the right side, second iteration, it goes to the left side.. you do this till you are left with the last three numbers. The last turn, you add the first number to BC, and depending on which side's turn it is, you send the next number there. And the last number to whichever side is left. Voila!!

Example, we build a 5 sided equal-sum-sided-triangle. 

Step 1: add 1,2,3 to vertices A,B and C respectively

Step 2 : next numbers to fill : 4,5,6 . First iteration, we start with right side. AC gets 4. Middle number always to the horizontal side. So 5 goes to BC. And 6 to the left over side , side AB. 

Step 3: next numbers to fill : 7,8,9. Second iteration , so we start with the left side. AB gets 7. As usual BC gets 8 and AC gets 9. 

Step 4: we have reached the last three numbers ( each side already has 4 numbers each ) numbers to fill in : 10,11,12. Because it is the last step, the least number goes to BC. Add 10 to BC. This is iteration 3. Odd iteration, meaning right side's turn. So next number 11 goes to side AC. And 12 goes to AB. Done.. How simple was that now!

Remember the fun part is, you can extend this magic triangle to any size and you do not have to break your head over a gazillion trial and error combinations.  Phew!! How cool is that now!! You know magic too now. Mathematical magic.. hocus pocus dabba dooo... let the magic triangle appear through!