Three athletes (and only three athletes) participate in a series of track and field events. Points are awarded for 1st, 2nd, and 3rd place in each event (the same points for each event, i.e. 1st always gets “x” points, 2nd always gets “y” points, 3rd always gets “z” points), with x > y > z > 0, and all point values being integers.
The athletes are named: Adam, Bob, and Charlie.
Adam finished first overall with 22 points.
Bob won the Javelin event and finished with 9 points overall.
Charlie also finished with 9 points overall.
Question: Who finished second in the 100-meter dash (and why)?
I enjoyed this puzzle so much that I shared it with (and discussed it at length with) my smartypants puzzle-sharing group. Now it’s your turn. The answer, plus a full explanation, can be found on the other side of the link, but I’d recommend that you try to solve it yourself first. If it seems impossible at first glance, start by breaking it down into what you can know, and what you can almost know, and work from there. Good luck!
Last weekend, I was cycling through Oxford, as I do, enjoying a reasonably leisurely pace. I say leisurely, but it’s been my experience that compared to the cyclists in Aberystwyth, where the city planners decided to build every single road on the side of a hill, the cyclists in Oxford are somewhat… wussy. They’re numerous, certainly, but very few of them actually put their backs into the activity, instead preferring to crawl around at a frankly pedestrian speed along their overcrowded cycle paths.
On several occasions, I’ve routinely seen people get off their bikes and push to get up even mild to moderate slopes like that outside the hospital, around the corner from Earth. The slope is long, certainly, but these people aren’t even giving up half-way… they’re giving up at the bottom! It just makes me want to send them to Aber for a few years to learn what real hills look like.
So there I was, cycling into the city centre, overtaking other cyclists as I went, when another cyclist… overtook me! This was only the second time this had ever happened to me since I moved to Oxford last summer. The other time, like this one, the perpetrator was a fit, lean young man, clad from the neck downwards in skin-tight lycra, donned with a streamlined helmet and riding a bike that just screamed out that it wanted to be raced. It was almost begging me to give it a challenge. So I did.
I guess part of me was offended that he happened to have come across me on a day when I was taking it easy. Traveling to and from work, for example, I’ve been pushing myself: the other week, I beat my personal best, making the 2.4 mile journey from the Bodleian‘s bike sheds to my garage door in just a little over seven and a half minutes. How dare this… enthusiast… overtake me when I’m just on a gentle meander in the sun.
We were just pulling into high street when he passed me, buzzing past in his fancy orange-and-black cycling shorts like a bumblebee riding a bullet. Ahead, cars and buses were coming to walking pace, backed up as far as I could see as the bank holiday traffic ground what was once a trunk road into little more than a car park. Between the vehicles, cycles picked their way around, darting in and out of the lanes of traffic. This was to be our arena.
My pedals span as I dropped back into a less-comfortable gear, picking up speed and pulling around a police van to get right onto the tail of my opponent. His speed advantage had been reduced by having to evade a taxi cab, and within a few seconds I was able to pull up into the wake of his slipsteam. Ahead, a bus began to pull away from a stop, and he overtook it. Seeing my chance as the bus began to indicate, I went around the inside, pulling almost alongside him as we streaked across the first of the pelican crossings and into the next block of traffic. Car, car, van, car, bus… we passed each one on one side or the other, and I occasionally caught a glimpse of the young man with whom I was competing.
Up ahead, the second pelican crossing switched to red, and we pulled up to the line together. Surprised at having somebody alongside him, I think, he looked across at me, and looked even more surprised when he recognised me as the person he’d overtaken a little while back. He eyed up my bike, as if he were assessing his chances. He seemed confident: and why not – he was riding a lightweight racing bike, designed to make the most of every bit of its rider’s strength to propel it along. I was on a mountain bike, designed to be rugged and durable – multi-purpose, nowadays. Weighed down by mudguards and pannier frames, I didn’t fancy my chances either. But my bike was running very well – I’d recently stripped it down to its component parts, washed and re-greased each, rebuilt it and fine-tuned it – and if ever it was set up to take on this racer, today was the day.
The lights changed, and we were off. He wasn’t holding back, now, and by the time we were half-way to the junction with St. Aldates I was panting, gulping down air to feed to my legs, pumping away beneath me. Our routes sometimes put us side-by-side or one behind the other, sometimes put us on the other sides of lines of stationary cars, but always kept us in sight of one another. This was going to be close.
The lights at the junction were in our favour, and we both rocketed around into the downhill section at St. Aldates. Buses crawled along the street, but there was plenty of room on the wide, slick surface, so we accelerated as we shot down the centre of the road. Ahead, heat haze made the black surface glisten like oil, and I was suddenly aware of how much I was sweating. Summoning all of my strength, I stood up and leant forwards, searching for just another half a mile an hour to catch up with him; his slender bike and slender body cutting through the headwind and pulling away from me. It worked: by the bottom of the road, I was alongside him again, and we were almost to my destination: the bridge at the bottom.
“My stop!” I called out, holding my arm out to indicate (mostly to him; there were no cars behind us at even close to our speed) where I was to go. I came to a halt, glad that I’d thought to tune up the brakes during my recent maintenance. He pulled alongside me, and for a moment I wondered if he perhaps had the same destination as me.
“Are you in a cycling club?” he asked, and I noticed that he, too, was beginning to get out of breath – although not so badly as I was.
“No,” I replied.
“You should be!” he said, “That kind of speed, on a bike like… that…” He gestured to my bike.
As he sped away and I started to look for a place to lock up my bike, I felt a great sense of satisfaction and pride. I didn’t know that I’d be able to match pace with him, but through sheer grit and determination, I’d managed. And then, just as I was chaining my bike to a conveniently nearby fence, another thought occurred:
I was still holding the letter that I’d meant to post on my way here. The postbox was back at about the beginning of the race… you know; where I was slowing down to begin with.
After moving to Earth, one of the things I thought might be fun was to use the excuse of being in a new place to try out some new things. A quick Google around the area uncovered OxDisc, the local Disc Golf society, who meet once or twice a week in a park less than half an hour’s walk from my house. Given that all I knew about disc golf I learned from the summary at the top of the Wikipedia page for the sport, I knew… well, basically nothing except that it was like golf, only with a frisbee and target rather than a ball and cup.
Accompanied by Ruth and JTA, who I’d somehow persuaded to join me, I set out to try to meet some strangers in a park. Having only spoken to anybody associated with the group online (all of whom subsequently turned out to be on holiday or otherwise unavailable), all we knew was vaguely where we were headed and that we were looking for a guy called George: sure, no problem – how hard can that be?
Luckily, it turned out to be reasonably easy to find our contact: once we were in the vicinity, all we had to do was look for the guy carrying a bag full of frisbees. Here came my first surprise: players don’t use just one disc. Three is pretty much a minimum – a long-range, high-speed “driver”, an easier to control but still pretty fast “approach disc” (or “mid-range”), and a slow “putter”. Only the putter looked like any kind of frisbee I’d ever thrown before: the others looked more like a rubber discus that had been given a lip to make it throwable in the same way as a frisbee is. George lent us each a set of three discs, explaining some of the differences between them. Professional players can be found carrying a variety of different drivers with different weights (and weight distributions) to make them tend towards understability or overstability or be more or less suitable for hyzer, anhyzer, forehand, elevator, and other varieties of throw. Yes, they have their own lingo: and I thought that this would be like throwing a frisbee around a park.
We teed off on the first hole of one of the courses that the group sometimes take around the park: markers like a protruding tree root or a gap between a path and a tree marked the tees, and the targets were all particular trees. Some of the courses were set up such that it was actually impossible to see the target from the tee as a result of the intervening trees, and so – without a profound knowledge of the course nor the sport – I had to fall back on a strategy of “throwing it sort-of in the right direction” as best I could and hoping.
Needless to say, my very first throw was a disaster. Unfamiliar with the unusual weight balance of the faster discs (some of which were “overbalanced”; that is, if you throw backhand using your right arm, as most people normally throw a frisbee, it will tend towards the left given an even spin and a level takeoff… are you following all of this? I certainly wasn’t), I was doomed to balls up my first throw… it rocketed forwards and then suddenly flew off to the left, diving deep into a forest of waist-high nettles. About 30 seconds later, I began to really regret choosing to wear shorts for this particular adventure, as my lower legs were rapidly becoming a mass of nettle stings.
Some of the other folks were obviously far, far more accomplished than any of us. Several times, we saw frisbees thrown end-on, like darts, flicked into the air where somehow they’d magically stabilise at exactly the right height to clear a particular obstacle. On a few occasions, the other players would fling their discs in physics-bending ways, turning right to avoid an obstacle then slowing down and turning left to clear the other side of it. Once, I even got to watch a guy deliberately throw his frisbee upside-down in order to “skim” it under a bush and right up to the target tree!
I was pleased with myself that by the end, I could generally throw the mid-range approach disc in a vaguely straight line, some of the time, and that once, I managed to pull off a hook shot up and over (and around) an inconveniently-placed copse, landing the frisbee almost exactly where I wanted it. But just the once, mind.
JTA seemed to pick up the sport pretty quickly, and on the long straight sections easily outperformed me (although I think I had more accurate “putting” ability). Ruth had somewhat more difficulty: the difficulties with her wrists left her unable to “snap” the disc out of her hand, which resulted in far slower throws. Nonetheless, we all had a good time and we’re talking about going along again… right as soon as we’ve had the chance to get a bit of practice in, so we don’t look like quite such wallies!
At the end of the evening, we were surprisingly more well-exercised than we expected (considering that it’s a sport of 5% throwing, 95% walking), and enjoyed the opportunity to calorie-up on ale and crisps at a nearby pub before making the trek home in the sticky warmth of the low sun.