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The Vanishing Numbers

REF: 120206

This case was one of the first mysteries that we ever solved. A very important set of numbers vanished into thin air leaving no trace.

We received a message from a distressed man named Robert. 

Robert’s wedding anniversary was approaching and he had been planning a secret trip abroad for himself and his wife Maria. In a secret phone call, Robert’s friend David, a travel agent, called up and gave him the number to book a bargain holiday cottage. David was calling from an airport as he was going away himself and wouldn’t be available for the next few weeks. He insisted that Robert call the number soon as the place would get booked up quickly.

Robert wrote down the number on a notepad in the kitchen across the top of the page, above his shopping list. 

At that moment Maria and Phoebe – their 7 year old daughter – were on their way down stairs. Robert closed the pad and pretended to be doing something else, and they all got ready to leave the house. 

As Robert was unlocking the car for Phoebe, he realised he had left the notepad in the kitchen. He said to Maria that he would just go in and grab his shopping list, but Maria offered. He was worried his secret would be exposed but she returned after a few moments and casually tossed the pad in the back of the car.

After Robert had dropped off the girls he got out the pad to book the cottage. But when he opened it, the phone number had completely vanished. The shopping list was there but where he had written the number it was empty. He frantically checked all the pages, even for an imprint on the page, but there was nothing.

We took up the case as a matter of urgency. How could a set of numbers, written by hand, suddenly vanish from a page without trace? Initial ideas sprung to mind, but with a few quick emails eliminating the possibility of invisible ink, hallucination and other formulaic suggestions, we went back to square one. 

The numbers could not have disappeared by magic, yet they had left that page sometime between their writing in the kitchen, and Robert opening the pad in the car to make the call. One of our team suggested a focus on the car journey itself. From Robert’s description of events the pad was left unwatched on the back seat for the duration of the drive. Was it possible that Phoebe had altered or rubbed away the numbers while Robert and Maria drove on unaware? 

However, it was duly noted that even if Phoebe had an eraser to hand, that there would be an imprint left on the paper and even on the page beneath. But as Robert had stated he had frantically checked for such evidence finding nothing. Although this thought originally seemed like a dead end, it led to our first real idea:

Robert, are there any more of these pads in the house?

Roberts reply was hugely revealing:

Yes there are two, we bought one for Phoebe for a school science project she is working on and one for us to use as a pad in the kitchen. Does that help at all?

We continued with this line of thought. Was it possible that because there were two identical pads that Maria had simply picked up the second one? This was quickly dismissed because of the shopping list. Robert wouldn’t have written out his shopping list twice in separate places. As we were discussing this idea, we received a surprising email from Robert.

I don’t think you will believe this, but Phoebe came to me this morning and told me that one of her drawings has vanished from her drawing pad. Her school project is on Space and she has been working on pencil drawings of the night sky. She says she was was about three quarters of the way through working on a replica of Orion’s Belt a few days ago, and now it’s gone.     

This information pieced together an idea so simple that we were surprised we didn’t see it in the first place. How could a number appear then disappear with the aid of Orion’s belt? Perhaps if Orion’s belt was drawn in pencil.

It seemed then that the key to the case not so much in how the numbers had gone missing, but why. Our next question was crucial:

Robert, do you remember what your wife was wearing on the morning you wrote the numbers? If you do, could you please go and inspect the garment, without getting yourself caught.

Robert’s reply was rapid, but he didn’t hide his confusion:

I found the jacket she was wearing and inside was this dark, grey powder all over the inside lapel and the inside pocket. Maria is not somehow involved in this is she?  

We were confident now that we were complete. We made the logical jump, and sent Robert our solution. And as it turned out, we were right.

Our final email to Robert read as follows:

Dear Robert,
The solution to your mystery is contained within Orion’s belt, plus the fact that you have two identical note pads.

We believe that Phoebe, not seeing the difference between the two pads had accidentally used the pad in the kitchen for her science project. We assume she turned to a blank page in the pad and drew her piece. But here two crucial things had taken place, she drew on the back of one of the pages, and in her artwork she had been drawing not just the stars but the entire night sky around them.

What would the back of a piece of paper, almost entirely covered in pencil create if turned back and written on from the other side? A carbon copy.

When you were making your shopping list, you opened the note pad turned to a blank page, not realising Phoebe’s drawing was on the back, and wrote out your shopping list. The list was then copied identically on the page beneath. But if so, why didn’t the phone number print as well? Because as you told us Phoebe was only three quarters of the way through her drawing. The top of the page where you wrote the number didn’t have any pencil behind it, and so the number wasn’t copied underneath.

So then how did the original numbers vanish? Simply, the original page, with both number and shopping list had been torn out, leaving you with only the copied shopping list beneath and Phoebe without her drawing, two missing items as one.

And here we turn to Maria. The residue you found in Maria’s jacket was not powder, but pencil, rubbed off from the drawing of Orion’s belt, torn out, folded and placed into her jacket pocket the day you went out together. She had probably overheard you on the phone with David, and our thought is that she has already booked a secret holiday trip for you both. She was the one who had removed the page before you left that day in the hope of stopping you from booking the cottage.
Happy anniversary.