Free Born on a Blue Day: Inside the Extraordinary Mind of an Autistic Savant by Daniel Tammet Page A

him too, and then the half-bubble men shake hands with each other. That would make six handshakes between four people. I continued in this way, imagining two more men in two other half-bubbles, until there were six in all and fifteen handshakes between them. The sequence of handshakes looked like this:
    1, 3, 6, 10, 15 …
    And I realised that they were triangular numbers. These are numbers that can be arranged to form a triangle when you represent them as a series of dots, like so:

    Triangular numbers are formed like this: 1+2+3+4+5 … where 1+2 = 3 and 1+2+3 = 6 and 1+2+3+4 = 10 etc. You might notice that two consecutive triangular numbers make a square number e.g. 6+10 = 16 (4 × 4) and 10+15 = 25 (5 × 5). To see this, visually rotate the six so that it fits into the top right corner above the ten.
     

    Having realised that the answer to the handshakes puzzle was a triangular number, I spotted a pattern that would help me to workout the solution. First of all I knew that the first triangular number – one – starts at two people, the fewest needed for one handshake. If the sequence of triangular numbers starts at two people, then the twenty-sixth number in the sequence would coincide with the number of handshakes generated by twenty-seven people shaking hands with each other.
    Then I saw that ten, the fourth number in the sequence, has the relationship with four: 4+1 × 4/2, and this held for all the numbers in the sequence; for example fifteen, the fifth triangular number, = 5 + 1 × 5/2. So the answer to the puzzle is equivalent to 26+1 × 26/2 = 27 × 13 = 351 handshakes.
    I loved doing these puzzles; they stretched me in a way that the maths I was taught in school did not. I spent hours at a time reading and working through the questions, whether in class, the playground or my room at home. Within its pages I found a sense of both calm and pleasure and for a while the book and I became inseparable.
    One of the greatest sources of frustration for my parents was my obsessive collecting of different things, such as the shiny, brown conkers that fell in autumn in large quantities from huge trees that dotted a long road near our house. Trees were a source of fascination for me from as far back as I could remember; I loved rubbing the palms of my hands into the coarse, wrinkled bark and pressing the tips of my fingers along its furrows. The falling leaves formed spirals in the air, like the spirals I saw when I did divisions in my head.
    My parents didn’t like me to go out on my own, so I collected the conkers with my brother Lee. I didn’t mind – he was an extra pair of hands. I scooped each conker up from the ground in my fingers and pressed its smooth, round shape into the hollow of my palm (a habit I have to this day – the tactile sensation acts as a kind of comforter, though nowadays I use coins or marbles). I stuffed my pockets one by one with the conkers until each was bulging full. It was like a compulsion, I just had to collect every conker I could see and put them all together in one place. I pulled my shoes and socks off and filled them with conkers too, walking barefoot back to the house with my hands and arms and pockets crammed full to overflowing.
    Back at the house, I poured the conkers out onto the floor in my room and counted them over and over. My father came up with a plastic bin bag and made me count them into it. I spent hours each day collecting the conkers and bringing them back to my room and the rapidly filling sack in the corner. Eventually my parents, fearful that the weight of amassed conkers might damage the ceiling of the room below mine, took the sack out to the garden. They indulged my obsession, allowing me to continue to play with them in the garden, but I was not to bring them into the house in case I left any on the floor for my baby sisters to choke on. As the months went by, my interest eventually waned and the conkers became mouldy, until finally my parents arranged for