
It's been a puzzling life: Interview with Trevor Truran  Editor at Puzzler MediaSunday, March 10, 2002Very appropriately, as some would say, On April 1st, known in the UK as April Fools Day, the firstever THUD tournament was held in the back room of a pub in Wincanton, Somerset. THUD is a new strategy game, invented by Trevor Truran, from the writings of Terry Pratchett in his worldfamous DISCWORLD series of books. In that strange planet carried on the back of four elephants standing on a giant turtle, trolls, dwarfs, werewolves, as well as humans, can all be found strolling the streets of the main city, AnkhMorpork. The game is a reenactment of a famous battle, at Koom Valley, where a small force of trolls came up against a large band of dwarfs. No knowledge of Discworld is needed to play the game and the 36 contestants of a special ‘quickfire’ tournament showed all the classic abilities of the strategy games player. Two battles were fought in each of three rounds. For THUD is an unusual game in that the players have to fight two battles – taking opposing sides in turn – in order to win the game by a combined points decision. The game is also unusual in having opposing armies of different numbers, moves and strategies. For games players, THUD offers the opportunity to independently create tactics and strategies in a game of skill that is very easy to learn. Astonishingly, at the tournament, several players were given a demonstration of the rules and, only ten minutes later, were playing in the first round. Always bumping into thingsdictate fact; learn fact; have test on fact"Somehow I survived grammar school, where the school motto should have been ‘fear is the key’" he says, leaving a lot of space for readers’ imagination. "Teaching was on the simple principle of dictate fact; learn fact; have test on fact; have exam on all facts. Terry Pratchett himself came along to present the trophies to the winners. Plans were also confirmed for an International Thud Tournament at the Discworld Convention in August. A fan’s report on the tournament weekend can be found at www.discworld.rapidial.co.uk. As a school teacher, his whole mathematics curriculum was based on games and puzzles. Looking back over 60 years of his own life, and 20 years affecting the lives of children as a teacher, Trevor Truran, editor of Puzzler Media’s Hanjie magazine in the UK still finds it astonishing how profound an effect games and puzzles can have on our lives. "I was, and remain, appalled that for the vast majority of teachers, such materials were only used at the end of term to keep the class occupied while the teacher marked exams and wrote reports" says Truran, who in his final year in college had developed a system of teaching a whole maths syllabus starting from a game or a puzzle. Later he used his "problem solving" teaching method to make schoolwork more enjoyable to some of his pupils, who otherwise would have found it a nightmare. Truran was born "at home during an air raid in 1942 on and under the kitchen table". The logical nature of his mind, Truran says, was already in place. He recalls wondering what possible difference the thickness of the kitchen table would make to a onethousand pound bomb coming through the bungalow's roof. He is also convinced that the shocks caused by ongoing explosions accounts for the fact that he "arrived on this earth about two inches away from everywhere else" – which is probably the reason why he is always bumping into things. Having his own special way of saying one thing and meaning another, Truran has no problem telling the story of his life, which in itself is like a very complicated puzzle. As soon as he was born, his mother was taken to hospital and later he was evacuated to near Liverpool, on the grounds that it was being bombed even more than London. He also knows his parents missed him a lot during World War II because as soon as it was ended, right in 1963, they sent for him immediately… "Somehow I survived grammar school, where the school motto should have been ‘fear is the key’" he says, leaving a lot of space for readers’ imagination. "Teaching was on the simple principle of dictate fact; learn fact; have test on fact; have exam on all facts. Failure in any part meant detention after school (45 minutes of painful writing and the train home missed). Three in a week won the prize of going in on Saturday morning and three of the latter resulted in the cane! Fortunately, I only ever received the first punishment". "One brilliant teacher got us all through our History GCE exam by dictating complete essays on ‘likely questions’. It didn’t matter that we only did half the syllabus and that whatever the wording of the question was; we simply had to latch onto the key name or event and write our memorised answer. Fortunately, I had a very good memory. So I left school remembering a lot of facts but not knowing, or having any passion, for anything". Where are the lights?After his school days, Truran decided to follow in his brother's footsteps and go to sea, if only to "catch up with him" and tell him: "I didn't need any more Hawaiian shirts". "Apparently", he remembers, "if you wanted to stroll around the bridge of a ship shouting 'hardastarboard' and 'splice the mainbrace' you had to be able to see the lights of a fishing boat three miles away at night. At the start of the test I was asked if the red light was right or left of the green light  my reply 'where are the lights' convinced the authorities that I'd never make third mate let alone captain. Fortunately, Radio Officers could be almost blind and, as every sailor knows, are completely mad, so I was ideal "Sparks" material. I worked for some years on RFA's (Royal Navy supply ships) and fought nobly for my country by sailing round and round Iceland in the Cold War and steaming up the Persian Gulf in the Kuwait Crisis (1960's version). Invalided out after a long stomach illness, I retrained as a maths teacher". The combination of the wonders of modern mathematics and Martin Gardner's books on recreational mathematics completely transformed Truran's thinking and showed he had his talent for games and puzzles. Ever since then it's been a "completely puzzling life  studded with a whole series of lucky breaks". How did you get your first job in this field? Newspaper to read on the train"The ultimate stroke of luck was, when travelling to a meeting about my puzzle book, Masterful Mindbenders, I bought a newspaper to read on the train". "To begin with, I happened to see a magazine I'd never heard of, and it was the particular edition that asked for contributions! This led to the publication of several new games and game analyses. About to take up a post as Readers' Games editor, it happened that a new puzzles editor would be needed soon  would I try making up puzzles instead of games and see how it went? Would I  notatall! A most enjoyable association with Games & Puzzles magazine and its editor, David Pritchard, was under way". Soon after, he took up the reins of a Puzzles Editor, a new computer magazine called to ask for a column on recreational mathematics. The editor, thinking it was a shortterm contract, asked him to have a go. Truran says he wrote and dictated his first column in a few hours and thought that was it, but it did come to an end only more than 13 years later. During that time he had introduced Rubik's Cube to a wider audience in the U.K., and created many new puzzles and games. This included one of the earliest ("maybe the first, who knows?") crossreference puzzles  which led him to create several more types, which belong to the same group as Conceptis' pictureforming logic puzzles. "The ultimate stroke of luck" Truran says, "was, when travelling to a meeting about my puzzle book, Masterful Mindbenders, I bought a newspaper to read on the train". This was the only paper he bought that year or since, since he later found he was "allergic to a chemical used in newsprint". The newspaper contained a logic puzzle to advertise a new magazine. "Had it worked, I would have solved it and forgotten it. But it didn't! Instead of complaining, I wrote politely and offered sample puzzles. The company was Keesing UK and soon I left teaching to work for them fulltime as a compiling editor for logic and maths. 16 years later, I'm still there, plugging away, although the company has been taken over and is now Puzzler Media. Doing your hobby all day long is not a bad way to pass your working life". Truran still finds it remarkable that maths textbooks once used games and puzzles only as intermittent 'interest' pages, breaking up the chapters on fractions, decimals and percentages. "It really didn't say much for the content of the book that only half a dozen pages were deemed to be interesting" he says in his understating manner. Truran claims two "blinding conversions" influenced his course of life. The deepest obligationFamilies of triangles and hexagons"Like everyone else, I guess, when confronted with the article on Golomb's pentomines, I wondered what would happen if shapes other than squares were joined together. I created families of triangles and hexagons and devised puzzles and games to play with them" According to Truran it all started back in the mid 60's at Christ Church Teacher Training College, in Canterbury, Kent. After his mathematical conversion had been blindingly created by 'modern maths', which made so much more sense than all the dreary rote learning he had gone through at school. "We were assigned the task of taking any mathematical book and preparing a review to be given to the group": says Truran, "Bad enough as that assignment was  we were required to buy the book we chose. My response was to scour the bookshop shelves for a Penguin paperback (always the cheapest option), with 'Mathematics' in the title. I came across 'Mathematical Puzzles and Diversions' by Martin Gardner from his articles in Scientific American, published by Bell and later by Penguin in 1961, as the first of a whole series of books of his column in Scientific American". Truran feels he owes Gardner the deepest obligation for changing the intellectual course of his life. "My teachers at college, in particular Eddie Williamson, who introduced me to modern mathematics and encouraged my original approach, set me on the course of becoming a teacher who had a passion for the subject and a desire to communicate that passion. Martin Gardner's books provided both the basis for the content and a mental spark. He is, without doubt, the greatest contributor to recreational mathematics since Henry Dudeney and Sam Loyd". His second blinding conversion occurred on the train journey home as he leafed through this book. What exactly happened on that train? "Well, I started to create mathematical ideas instead of receiving them and learning them by rote just to pass an examination and gain a piece of paper saying I'd done it. Until then all learning had been a matter of being given information and facts and using them, though hardly ever, if at all. How many people calculate the height of a tree using Pythagoras? I began, immediately to ask 'what if...? That has been the basis of my creative life ever since. Take a given situation and ask the question 'what if?' I realised then that mathematics was something you DID, not just something you learned from what other people did." Within days he had made games and puzzles from the book and had begun experimenting. Soon Truran was making up new games, puzzles and teaching materials, a habit he still can't break today; "Like everyone else, I guess, when confronted with the article on Golomb's pentomines, I wondered what would happen if shapes other than squares were joined together. I created families of triangles and hexagons and devised puzzles and games to play with them". Later Truran found out that many other people had also done the same thing, but it didn't matter one bit. He had INDEPENDENTLY created something mathematical, and, as it turned out, a few original puzzles and games, and that was IT. "The absolute essence" he points out, "is that I had done something creative on my own. This was a feeling I tried to get across to my pupils". Some of the pupils must have had more difficulties than others. How did the class accept them? "I was very quick to stop any class derision of a pupil who had suggested an idea which was, in fact, not valid. Whenever the class laughed at someone, I would point out (a) that's the first idea anyone in the room has had and (b) you PROVE it wrong! I always welcomed and praised any idea from a pupil and required the class to take it seriously. Pupils soon learned that every idea is worth exploring  if only to find out a way not to go". Ah  what a night!Truran still finds it remarkable that maths textbooks once used games and puzzles only as intermittent 'interest' pages, breaking up the chapters on fractions, decimals and percentages. "It really didn't say much for the content of the book that only half a dozen pages were deemed to be interesting" he says in his understating manner. Truran claims two "blinding conversions" influenced his course of life. One day Truran began the ordeal with a topological puzzle from Martin Gardner, apparently an older puzzle that Gardner wrote about and an example of Dydeny's 'buttons and string' method. Swithching puzzleSwitch the three red counters with the three blue counters by moving the counters, one at a time, along the paths marked by the straight lines. In one move, a counter may pass through several circles, but it may not pass through, or land on, an occupied circle. What is the smallest number of moves required? "Imagine a rectangular layout of points (circles) 4 columns by three rows. Three red counters at one end are to be interchanged with three blue counters at the other end in the minimal number of moves. The circles are joined by lines in a crisscross pattern. In topological terms this means that apparently separated places are in fact close together (because of the line connecting them) and neighbouring circles are really far apart. By topologically untangling the connections the simplest solution can be determined. In his final year in college Truran was invited to lecture on using games in mathematics for the area Teachers' Association and had developed a system of teaching any part of the syllabus starting from a game or a puzzle. "Ah  what a night!" he remembers, "When the teachers came in and sat down expecting a lecture, they were faced, instead, with 15 counters between each pair and I invited them to play a game based on a puzzle, described in Dydeny's book as 'the pebble game'. Given 15 counters, two players take turns to remove 1, or 2 or 3 counters. This is repeated until all are gone. The player with the ODD number is the winner. The original puzzle simply required the solver to work out the first move that would guarantee the first player a win. The teachers played the game and then I followed up with a demonstration of all the mathematics that could be derived from a study of the game. Later in school this would extend to a full term's work. How can you tell if you have won without counting the number you have taken? Why must the game start with an ODD number? This leads into NUMBER SHAPES  rectangular numbers, the properties of odd and even numbers, adding such numbers, showing, through counters that ODD+ODD= EVEN, leading into an exploration of other number 'shapes'. A full term's work"The teachers played the game and then I followed up with a demonstration of all the mathematics that could be derived from a study of the game. Later in school this would extend to a full term's work." It also leads to PROBLEM SOLVING TECHNIQUES  15 is a lot of games to slog through, so break the problem down by starting with fewer counters, work your way up and look for a pattern  the heart of mathematical activity. With 1 counter only, first player wins by taking 1. With 3  by taking 3. But who wins with 5? Here we go into the nature of proof by citing all cases. The second player is a certain winner. Who wins with 7? The use of discovered rules to extend our knowledge. It can be proved that a player with an even number so far and leaving 4 or 5 can be sure to win. So with 7 at the start  take 2! Further exploration will show that the winning ' first move' for a game of any number of counters depends on dividing the number at the start by 8. MODULO 8 arithmetic arises naturally and usefully, not as a page in a text book started for no reason. The sequence of moves needed to win the game can be explained by MAPPING DIAGRAMS. In fact, the whole strategy for any game with any number at the start can be expressed by a few mapping diagrams. Modulo 8 leads into group theory... Phew! Enough to keep a class doing and learning mathematics for a long time, and all you need are some counters, a game, and a willingness to explore". Have you got any more?Working at 'my' problem on the blackboard"When the children came in, I would totally ignore them. Instead I would carry on working at 'my' problem on the blackboard. It was never long before the clamour to know what it was all about became far louder than the chatter of those who thought their prayers had been answered and there'd be no work that day." Back in the 1970's, for 11 to 16 yr olds, the syllabus was very much exam driven and the teacher's responsibility was to get the children through the exams, if possible, and not to be too concerned with awakening their minds to the wonders and pleasures offered by mathematics. "Some schools were less than brilliant as far as I was concerned" says Truran "it was just that I could make schoolwork more enjoyable to some, who otherwise found it an unhappy time of life". Time devoted to puzzles was limited but Truran got round that by introducing the then novel idea of 'problemsolving.' The effects on some of the children were dramatic; "Discipline problems were eased, lessons became actually enjoyable, not the least for the less able for whom conventional mathematics was a nightmare" he says, still full of enthusiasm. "One example sticks in my memory still. I had as a pupil a tough 14 yrold miner's son who found all school work, from reading onwards, as unpleasant as having a tooth out without anaesthetic. A maths lesson with him consisted of both of us hoping to survive the hour still in the same room and for me that the rest of the class might gain something." "For this particular pupil" says Truran, "the uncanny thing was that he mentally did all the untangling and found the solution  though he couldn't explain it in mathematical terms. I reckoned 15 minutes to draw the diagram, probably 15 more to get the moving rules across to everybody, followed by half an hour of relative peace while they sought the solution. After a couple of minutes he came up to my desk, plonked the board and pieces down and said: 'done that!  have you got any more?' He then demonstrated the solution and from then on, provided he was given the material as a puzzle, not as something to learn or fail at, he was fine. Teaching 9 to 13 yrolds, later, and by then in charge of maths, Truran was free, both from the restraints of exams and imposed syllabuses, to fully develop the system. Asked what his aims were, he always used to reply: 'To get children running down the corridor to the maths lesson just as they run away from it to PE (physical education)'. Start the topic with a story, a game or a puzzle" he specifies "and the mathematics followed automatically. All sorts of tricks could be used to get their interest and to show them that mathematics was something you did for pleasure, not just a chore to be undertaken on orders from a higher authority" Like What? "When the children came in, I would totally ignore them. Instead I would carry on working at 'my' problem on the blackboard. It was never long before the clamour to know what it was all about became far louder than the chatter of those who thought their prayers had been answered and there'd be no work that day. Reluctantly, I would explain my problem and finally agree that they could help me solve it, if they liked. The lesson was under way without anyone realising it". The arrival of computers greatly added to the range of puzzles and games that Truran could be offered. He soon latched onto programming in BASIC and puzzles that had taken lots of work could be colourfully presented and animated in a simple way. Mathematics is a complete waste of timeWhen did you do any more?I would ask those parents (and frequently did) WHEN WAS THE LAST TIME THEY EVER USED ANY OF THE MATHEMATICS THEY HAD LEARNED IN SCHOOL? Go on  unless it is for a particular profession, when did you do any more than combine numbers, tell the time and work out your money? Tell me when you last used simultaneous equations, trigonometry, Pythagoras, long division, logarithms, and angles of a triangle? One 9 yrold found ordinary maths so difficult that for the whole of the first year he wouldn't even speak. Nothing would draw him out until Truran sat him in front of the computer and called up a simple number puzzle that required some decisionmaking. "Can I do that next time?" The 9 yrold asked at the end of the halfhour. "He'd not only spoken but had made more decisions in half an hour than he had, probably in all our previous sessions" says Truran. It almost sounds too good to be true... It isn't simply that games and puzzles can turn a lad like him into a mathematician, but that they offer a situation without the usual tension and fear of failure that goes with many conventional courses. But this also can be described as a waste of time... "Why do we place so much emphasis on our child being good at maths? If he couldn't draw or paint (as I can't) are we complaining to the Art teacher? We are all good, hopefully, at something. School is to find out what. I would promise to do my best to get every pupil as capable at the fundamentals  numbers, money and time, so that they could cope in the practical world. For the rest, I wanted to encourage a method of thinking, of being both logical and creative. P.S. I used to be very concerned that in all formal teaching we assume that the pupils are logical  without ever feeling the need to teach logic. I found that some teachers could have benefited from the formal logic I taught in my maths lessons. Logical thinking was a fundamental part of the course and I never assumed that it 'was obvious'. One funny story, if there is room. In order to introduce the concept of multibase arithmetic (binary etc) I told the children a story about a group of Eskimos  the UBBERBLUBBER Eskimos. They had only six fingers (having evolved a long time ago from a group who found that if they wore mittens they couldn't fire their harpoons, but if they didn't their fingers froze, so they wore just one mitten which evolved into a single finger and one ungloved hand (so they were halfstarved and halffrozen … mad. But of course this is not the whole story). Anyway, from this developed a system of BASE SIX arithmetic, complete with Eskimo signs for digits and all the works. At one Parents Evening a couple came up, slapped their child's book down on the table and said  'About these Ubberblubber Eskimos  why are you teaching it? MY KID'S NEVER GOING TO GO THERE!" But still, some people might say "Hey! I want my child to learn real maths in school, not just play with puzzles" Didn't you have problems with some of the children, parents, or other parts of the education system? I would ask those parents (and frequently did) WHEN WAS THE LAST TIME THEY EVER USED ANY OF THE MATHEMATICS THEY HAD LEARNED IN SCHOOL? Go on  unless it is for a particular profession, when did you do any more than combine numbers, tell the time and work out your money? Tell me when you last used simultaneous equations, trigonometry, Pythagoras, long division, logarithms, and angles of a triangle? For most people  when did you last do multiplication without having to pick up a calculating machine? Of course mathematics is a complete waste of time  just as playing a musical instrument, or painting a picture, or writing a poem, or looking up at the stars or any human activity is a waste of time  or is it a way to learn about how your own brain works and in what particular ways it can add to the enjoyment of life. I was once told that teaching is the process of presenting a collection of windows to children  windows that, with my help, could be cleaned and looked through  in the hope that one or two or them would prove attractive and be thought enriching and worth looking through in more detail. Had PictureForming Logic Puzzles (particularly Conceptis puzzles that require only single line logic) been available to me when I was teaching, they would certainly have been an important tool in my problemsolving and logical thinking portion of the maths syllabus. I would have started off with very small and easy puzzles for 9 year olds and used them each year, progressing to more advanced puzzles according to age and ability. I would also have used them to challenge the logically able. A small puzzle would have been ideal in an exam to test a pupil's ability to think purely logically". What is the minimum age for children, for all this? An important tool of the maths syllabus"Had PictureForming Logic Puzzles (particularly Conceptis puzzles that require only single line logic) been available to me when I was teaching, they would certainly have been an important tool in my problemsolving and logical thinking portion of the maths syllabus." "Children of all ages and abilities benefited from games and puzzles  with some of the most able we were able to venture into group theory with 12 yrolds. With the relaxation and sense that maths is fun, the least able could develop some numbers and spatial skills that would help them later on". When you say puzzles  are you referring to puzzles in general or to maths and logic puzzles? "Oh, puzzles to me, always mean Maths and Logic  I tend to dismiss other puzzles as alright for some people but of little or no education value! Like, in a crossword, if you don't know the answer word or the fact behind a general knowledge clue, there is nothing your brain can do to get the answer. A logical puzzle can be solved by pure brain power  you can think up a way to do it without any external knowledge. However, I advocate solving any kind of puzzle (even wordsearches!) as a useful activity  in fact, part of my teaching philosophy was that mathematics is an exercise that helps the brain to function just as physical exercise helps the muscles. The more you exercise your brain (on what is secondary) the better and longer it will function. Elderly people, especially, can benefit from keeping the brain active through puzzles when the body is no longer up to the physical side of living. For me, games and puzzles led to an editorial post with Games & Puzzles, a column in a computer paper on recreational maths that ran for 13 years, a book, fulltime work creating, compiling and publishing logical puzzles and eventually to having a twoplayer strategy game marketed by Discworld. All this  and Conceptis Puzzles! It's been a puzzling life  thank goodness". About Gil GalantiGil Galanti is Marketing Manager of Conceptis Ltd. Gil is also runs a blog with his wife Nitsan at cultcase.com 