GC7QG2B - Henry’s Obsession II - The Letters!

After years of patient therapy, Henry has moved on with his life. His therapist is delighted! Henry no longer has any interest in switches at all! Instead, Henry's rather neat and unique mind has become fascinated with listing things in order.

It all started when, as he was cleaning out the debris from his former home following the incident with the chicken and the light switches, he dropped a dictionary. The spine split and several pages fell out. In his haste, he just bundled them all together and took them to his new flat.

Later that evening, he started to sort out the mess, trying to get the dictionary pages back in the right places. He found a strange, calming warmth spread through his mind as he perused the words and sorted them into order. Later that night, he found sleep eluded him as he couldn't stop thinking about words and letters and putting things in order.

Giving up on sleep at around 3am, he got up and made himself a nice cup of Horlicks. Sipping it in the dark, his mind turned the problem over. 'Just how many words are there?' he pondered. 'And how many words are possible? And how many words share the same letters?' He thought briefly about the word 'Horlicks' Obviously, the letters could be used to make 'Lick', 'Shock', 'Corks' and 'Loch'. Quickly he found over 150 other words that could be made, but not that elusive 8 word anagram that used all the letters.

Ignoring the fizzing and popping sensation in his brain that he hadn't felt since the light switches were new, he sat down and made a list of all the 40,320 permutations of HORLICKS. No good, there wasn't another word there.

Giving up at this stage, and with dawn peaking through the curtains, Henry went back to bed and dreamt of letters, words and lists. Rising late in the afternoon, he set to work. 'Horlicks' was all used up, so he started making lists of letters. 'A' was irritating. It was just 'A', you couldn't list it or re-order it at all. 'AB' was not much better, 'AB' & 'BA'. Not much scope there for anything more. 'ABC' was a step in the right direction. Henry was a little surprised how the permutations jumped from 2 to 6 by adding one more letter. 'ABCD' gave him 24. His interest grew and his tea went cold.

Rushing out to the newsagents on the corner, he armed himself with A4 pads and pencils and rushed back home. Before the sun went down, he'd worked out all the permutations of 'ABCDE' (120) and 'ABCDEF' (720). By dawn, without any thought of food, drink or sleep, the 5,040 permutations of 'ABCDEFG' and the 40 thousand permutations of 'ABCDEFGH' were listed in his neat, slanted script. A week later and he was finished with 'I' (360.000) and he needed to take a pause to stock up on new pads and pencils, get a shave and have something to eat - he'd lost a stone in weight since this started.

Nobody saw anything of Henry for quite some time after this, until one day, just as Mary, his former therapist, arrived home from work she saw him waiting on her doorstep. Dishevelled, half-starved with bloodshot eyes and ragged clothes, she hardly recognised him. Helping him inside, the story began to unfold. Between the twitches, tics, rambling mutterings and interrupted by long, vacant stares into space, Henry told his story.

He'd completed 'J', 'K', 'L' and even 'M'. The trouble was, in the six billion permutations of 'ABCDEFGHIJKLM' he'd made a few small errors. In just ten of the permutations he'd got some letters transposed and he couldn't get things sorted into order again.

Drawing out a grubby piece of paper, all that was left of a whole lorry load of A4 writing pads, he showed her a table of results where the errors lay.

"The problem is", he explained, "In each of these lines, I've swapped two letters round. If I knew how many letters lay between the transposed characters, I'd be OK - I could work it out. But how do I find out how many letters there are between the errors?"

Here is Henry's table. Can you help him find the answer he's been looking for?