GC7QHQC Henry’s Obsession III - Fewer Numbers

Henry has a Revelation

Henry had a really bad time after his new flat collapsed under the combined weight of about a million A4 notepads during his Permutations Phase. He pondered the problem whilst sitting in the waiting room of the Housing Association, before his interview with their insurance adjusters.

The problem was, there was just so much repetition! In his final exercise, most of the 13 character ‘words’ differed from the previous word by only two characters. He must have written ‘ABC’ out millions of times. Henry’s eyes glazed over as his brain, uncomfortable with the vague ‘millions of times’, focussed on the problem. After just a few seconds it popped up with the value of “39,916,800 times”. He couldn’t say how he knew that was the answer, he just knew it was right. That was the way his mind worked.

If only there was some way to write the numbers down with the absolute minimum of repetition…

He thought for a moment. Then, pulling out a piece of paper from his pocket (it happened to be a court summons arising out of a slight misunderstanding the week before), he started scribbling on the back.

“Let’s look at four digit numbers.” he muttered, causing the receptionist to look at him with narrowed eyes. “There’s ten thousand numbers, that’s forty thousand characters to write down. We start with four zeros,” and he wrote “0000” on the paper.

“Next comes ‘0001’,” he muttered, “but I’ve already got three zeros, so we just need the ‘1’.” Henry added a ‘1’ to the four zeros he had written already.

With a sudden surge of excitement, Henry realised that if he wrote those five digits in a circle, he could get five different four digit numbers from just those five characters: ‘0000’, ‘0001’, ‘0010’, ‘0100’ and ‘1000’. Instead of having to write 20 characters, he’d only had to write five!

Henry’s pencil became a blur. In what, to him, only seemed a matter of seconds his paper was covered with calculations and a long stream of ten thousand characters.

“Ha ha!” Henry shouted out in triumph. These ten thousand characters contained every single four digit number. Each one appeared once, and only once! What previously would have taken forty thousand characters had only taken ten thousand!

Henry rummaged through his pockets, looking for another piece of paper to start on the five digit numbers. All he could find was the restraining order taken out by Mary, his former therapist. Turning it over he quickly wrote five zeros on the top of the first page.

‘Only one hundred thousand digits!’ he thought, in triumph, ‘Instead of…’

Just then, he became aware of the receptionist standing over him, shaking him roughly by the shoulder. Wrenching his attention away from the stream of digits marching in procession across the front of his mind, he looked up, uncertain of his surroundings…

“They’ve been calling your name,” the receptionist snapped, “Over and over, for the last five minutes!”

Reluctantly, Henry abandoned his list and stumbled into the interview room to learn his fate…

To find this cache you will first have to complete Henry’s task. Then, the five digits for the Northings are to be found starting at position 79,703 and the five digits for the Eastings are to be found starting at position 18,827. You can assume N52 and W000.

You can see all of the caches in this series at the Henry’s Obsessions List Page

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