My friend Zeke couldn’t have been any more mysterious when he called. “Meet me at the corner of S37 53.519 and E145 14.198” he said. “And bring your GPSr.”
I got to the spot and saw Zeke standing at the side of the road. He was holding a large bag. I stopped the car alongside and hopped out.
“Whassup Dude?” I asked him.
“Hi Bro”, he smiled. “Good to see you. Thanks for coming”
“Hey, anything for you”, I said. I had met Zeke out bushwalking about five years ago. We had struck up a conversation and found that we had a lot in common. We have been good friends ever since. He was always a happy soul but he became quite serious for one of the few times I had seen since we first met.
“My father’s needs me back home” he said. “I have to go away for a while. There are a lot of things that I have to tell you. Stuff that I had hoped I would never have to bring up with you but I ask you to keep an open mind as this is going to blow your brain”
“Sure.” I said jokingly “Nothing that you tell me would surprise me”. What had he done? Robbed a bank? Run somebody over? No. Not Zeke. Never.
“Don’t be so sure” he replied, and his usual impish grin returned to his face. “Let’s start with this”.
Having said that, he pulled a small electronic beacon from his bag. It had a red flashing pulse light on the top of it. He then pulled what looked like a tube of glue from the bag, smeared a little onto the bottom of the beacon and stuck it to the middle of the footpath.
“You got me” I said. “I certainly wasn’t expecting you to do that”
“Oh, I’m not even up to the fun part yet. If you liked that, you’re going to love this.”
He then produced what looked like a television remote control from his pocket, pointed it at the beacon, pressed a button and it clean disappeared. It just faded out of existence.
“Whaaa?” I gaped, and I quickly bent down to touch the footpath where the beacon was. There was nothing. No trace. I turned back to Zeke.
“Where did it go?” “The reason you can’t see it because it’s not actually there yet” he said.
I looked at him blankly. Looking blankly was something I was apparently quite good at but I was about to get a whole lot better at it over the next hour or so.
“Here”, he said and he handed me a pair of goggles. Through them, I could see the beacon. I took them off. No beacon. I put them on again. Beacon.
“The goggles allow you to see a thousandth of a second into the future. I changed the chronotons of the beacon so it now exists in an ever so slightly different plane of existence. Before you ask, it won’t just reappear in a thousandth of a second’s time because I didn’t change the phasing. It remains just that little bit forward in time.”
“I see” I said.
“Great.” He replied. “Now that I have your full attention, the next bit is really going to freak you out so I need you to promise me that you won’t scream. Promise?”
“All I can promise after seeing that, is that I can promise you nothing” I said and I smiled weakly.
“That’s gonna have to be good enough” said Zeke, then he reached up his left sleeve with his right hand and peeled his hand off like a rubber glove. Underneath remained two long gangly bluish fingers. He held them up to my face so I can get a good look.
“Hooley dooley” I yelled as I staggered backwards. Zeke grabbed me from falling over and was urgently shooshing me to keep quiet.
“Hooley dooley” I whispered loudly. “What the heck, Zeke?”
“Okay, buddy. It’s okay. It’s a lot to take in. Let’s start at the beginning. Walk with me a while and I will tell you everything.”
We had any of four directions that we could have walked from the point that we were standing. Zeke picked up his bag and waited until a car had driven past, then he started to walk up the hill, in the same direction from which the car had originally come from. I dropped in alongside, unsure of how this was going to get any weirder. I was about to learn. Zeke slipped his two fingered hand back into his other hand glove.
“Boy, it took me a long time to get used to a five fingered hand, but I’ve got to admit that I love the opposable thumbs”. He saw that I was practicing my blank stare again so he continued. “Hey, my other hand only has one finger so just as well you... okay, okay on with the story” and I released the grip on his ear.
“My name, Zeke, is short for Zekianihel Brenzox. I was born on the planet Mathematasia. It is about 325 light years in that direction. I was posted here around ten of your years ago on a mission from my government to protect a technology that only two races in the known galaxy have developed. The races are Mathematasians and the Earthlings”
We had passed about three houses when he stopped, pulled another beacon from his bag, glued it to the ground and zapped it into the future. This one had a green light.
“Oh, by the way. This one transmits a number.” he said.
I glanced over his shoulder and saw him write the number eleven into a note book. We continued walking up the hill.
“What was the technology? I asked. “The simple calculator” he replied. “The planet of Mathematasia has been locked in a savage battle with our sister planet, Calculon, for over 500 years.”
We reached an intersection, the first we had come to. Zeke pulled out another red beacon and glued it and zapped it. Again we had a choice of directions. Zeke started downhill again but not in the direction from which we had come.
He continued the story “Both of our races had based our development on mathematics. There was much argument as to which planet had the higher mathematical standards. The Math Wars, now don’t look at me like that. This is serious. The Math Wars were conceived as a series of mathematical puzzles that were to be fought between our two races. Whichever race won the Math Wars would rule both of our planets for the next five years.”
About halfway down the hill, Zeke stopped, placed another green beacon. “The number on this one is double the number of the last one.” he said.
He wrote another number into the book which I saw was twenty two.
“Yep, I can see that.” I said as I pointed to his book.
“Hey, don’t look at this. It will only confuse you.” he said, and he slipped the notebook into his pocket again. “Now, the wars were fairly even for the first hundred or so years. We won a couple, they won a couple. Things were good. Then one war, they developed some sort of mind enhancing drug. They won war after war and things started to change.”
We reached the next intersection. Zeke placed another red beacon. We set off again in a new direction downhill once more.
“They started to get cocky. The Calculons started to make the Mathematasians do all the menial work. You know, accounts payable, BAS forms, checking shopping dockets for overcharges, you know, that sort of thing.”
We were halfway to the next intersection and Zeke placed another green beacon.
“This is double the last one. Remember that. For over 150 years we slogged away as we gradually became their slaves. We were a lost race. Then one fantastic day, one of our scientists came up with the discovery of a lifetime. The calculator.”
At the next intersection, Zeke placed one more red beacon. We walked uphill from this point but not in the direction from which we came.
“With the aid of the calculator we surprised the Calculons at the next wars. We won. The Calculons soiled themselves literally. They were afraid that they were now about to receive all the rubbish jobs that we had received over the last decades. And we weren’t about to disappoint them. For the next 20 years, all the jobs that were originally assigned to us were now assigned to them.”
Halfway up, Zeke placed another green beacon. “Double the last one by the way.” And we continued on up.
“The Calculons were a very smart race mathematically, but unable to grasp the electronics of creating a calculator. They soon realized that they were never going to beat us and that their only hope lied in somehow coming into possession of one of our calculators. We ramped up security and they never did get hold of one.”
We reached an intersection. I was unsure what Zeke was doing with these beacons but I at least understood why he didn’t stop to place a red one here. Without breaking stride he started walking downhill once more but as before, not the direction from which we had come.
“After some time had passed, we had hoped that they had learned their lesson and we decided to treat the Calculons more fairly. We developed our sciences but we also kept some of the more security based jobs to ourselves and space exploration was one of those jobs. We discovered your planet some 30 years ago and we just gob-smacked when we found that Earthlings had developed the calculator independently of Mathematasia.”
Halfway to the next intersection, Zeke placed another green beacon.
“Half the number of the lowest beacon I have placed so far. Got that?”
We continued on.
“We were at least amused that you had named your discovery the “Calculator”. A very funny and ironic twist. Calculon – Calculator. Get it? Okay must be a Mathematasian sort of joke. We did not want to impede or interfere with Earth’s progress but at the same time, we could not trust that Calculon would not launch secret space exploration missions of their own and discover Earth and the Calculator.”
At the next intersection, Zeke placed yet another red beacon. Then we changed direction and continued walking downhill.
“If the Calculons do discover Earth, the future of both of our worlds may be in jeopardy. A Mathematasian agent was assigned to Earth to secretly monitor any approach of a Calculon craft. Unfortunately, he lost focus and became too engrossed in having too much, let’s say, fun. At least his identity remains a secret to humans.”
“It’s Bill Gates isn’t it?” I asked.
“Yes, no, yes, dammit. How did you work that out?” he stammered.
“Ha. I knew it. Explains heaps. Especially his two fingered typing style too” I laughed.
“Right.” Zeke had been enjoying having the upper hand and had been on a roll up until now. He placed another green beacon.
“Half the number of the last one. Are you remembering this?”
“Yes, please continue”, and I stifled another giggle. “Bill Gates, hee hee.”
“As I said earlier, I was sent to Earth about 10 years ago. I have been monitoring transmissions ever since. I now need to go back home and I can’t return for about 5 years.”
At yet another intersection Zeke placed one more red beacon then started uphill once more. As per before, not in the direction from whence we had come.
“Now, I have placed a transmitter box that will continue to monitor for Calculon activity. The box will need recharging periodically and this can be done by opening the clips on each side of the box. To make sure no Calculon sees you continually returning to the box, it will be safer if you can organise a different person to go to the box each time.”
“Cool, I can disguise it as a geocache and people will recharge it on each find.” I said.
At this point we were halfway to the next intersection. Zeke pulled out another green beacon, secured it and zapped it.
“This is the last one” he said. “This is the largest number of all. It is double the number of the largest beacon we have placed so far.”
“Cool” I said. “So where is the box?”
“Now, these are the co-ordinates. S37 5a.bcd E145 1e.fgh. To break the code, you will need to use a=59, b=127, c=80, d=125, e=116, f=127, g=125, and h=121.”
“But they are double and triple digit numbers” I said, “They need to be single digit figures to fit a set of co-ordinates”
“True” said Zeke, “And so they will as soon as you know how to manipulate them.”
“Struth. How do I do that? ” I asked.
“You should be able to work it out. Now don’t tell anyone what the co-ordinates are directly. Too risky.” he said.
“What should I tell them then? I asked.
“Just tell them exactly what has happened since we arrived. All the information is there. There are possibly five leaps of logic that someone will need to make to work it out. This should be enough to fool the Calculons. Now that’s it and I really need to get going. Bye and good luck mate. See you in five years”
“Bye, Zeke. You know I am really going to cop some heat for this one. The 13th Cache, The Valley Challenge and I don’t even want to bring up what happened with the Sherlock Holmes Series.”
“You’ll be fine” he said. “Take care” and with that he was gone.
Oh boy, oh boy. Now where is that box?
Hint 1 - added 22 Oct 06 - A few days later I sat at home at the kitchen table. I had just returned from my visit to the transmitter box. Since the time that I had last seen Zeke, I had puzzled over the location of the box. I had racked my brains day and night as to the five leaps of logic that Zeke had mentioned. When I had finally pieced it all together, I realised that I had touched on all of these logic leaps many times but it was only when I had linked it all together that it finally made sense. Only then, had I remembered that Zeke used the word “possibly” when he described the logic leaps and this is because the first leap was not 100% necessary but it did make the task a darn sight easier. That logic was “It is very unlikely, though not impossible, that someone is going to be able to work out the location of the box from home”. (Some days later Team Rubik proved that it was indeed “not impossible” to do just that, but boy, it would make life a lot easier to walk where we walked)
Hint 2 - Added 16 Nov 06 - I had also realised that by the time that Zeke left, I had also no need to work out the second leap of logic as I had been with Zeke as he walked the path around those streets. For those following, there would still be enough information to know where we went. Even if you knew where though, then why? Ah, that was the third leap of logic. There was nothing to see there physically in regard to physical clues. No co-ordinates. No boxes. Certainly no beacons (unless you had use of the goggles). The path definitely did not lead you to the box. It led just to a normal place on a normal street. So, was the path taking you somewhere or was it something else?
Hint 3 - Added 24 May 07 - I realised that the path would make a lot more sense if looked from the direction that a Mathematasian would first see it on arrival.