Again we have a puzzle from the Sherlock Holmes puzzle book by Dr. Watson (aka Tim Dedopulos).  This one is quite a bit more challenging, at least for me.

“When Holmes and I met with Wiggins one afternoon, he was accompanied by a rather scrappy-looking mutt, who eyed me with evident suspicion.

‘This is Rufus,’ Wiggins said. ‘He’s a friend.’

‘Charmed,’ I said.

‘He’s very energetic,’ Wiggins told us. ‘Just this morning, he and I set out for a little walk.’

At the word ‘walk’, the dog barked happily.

‘When we set out, he immediately dashed off to the end of the road, then turned round and bounded back to me. He did this four times in total, in fact. After that, he settled down to match my speed, and we walked the remaining 81 feet to the end of the road at my pace. But it seems to me that if I tell you the distance from where we started to the end of the road, which is 625 feet, and that I was walking at four miles an hour, you ought to be able to work out how fast Rufus goes when he’s running.’

‘Indeed we should,’ said Holmes, and turned to look at me expectantly.

What’s the dog’s running speed?”

Answer.

See the Rufus Puzzle for solutions.

Here is another problem (slightly edited) from the Sherlock Holmes puzzle book by Dr. Watson (aka Tim Dedopulos).

“Holmes and I were walking along a sleepy lane in Hookland, making our way back to the inn at which we had secured lodgings after scouting out the estates of the supposed major, C. L. Nolan. Up ahead, a team of horses were slowly pulling a chained tree trunk along the lane. Fortunately it had been trimmed of its branches, but it was still an imposing sight.

When we’d overtaken the thing, Holmes surprised me by turning sharply on his heel and walking back along the trunk. I stopped where I was to watch him. He continued at a steady pace until he’d passed the last of it, then reversed himself once more, and walked back to me.

‘Come along, old chap,’ he said as he walked past. Shaking my head, I duly followed.

‘It took me 140 paces to walk from the back of the tree to the front, and just twenty to walk from the front to the back,’ he declared.

‘Well of course,’ I said. ‘The tree was moving, after all.’

‘Precisely,’ he said. ‘My pace is one yard in length, so how long is that tree-trunk?’

Can you find the answer?”

Answer.

See the Tree Trunk Puzzle for solutions.

Again we have a puzzle from the Sherlock Holmes puzzle book by Dr. Watson (aka Tim Dedopulos).

“Our pursuit of the dubious Alan Grey, whom we encountered during The Adventure of the Third Carriage, led Holmes and myself to a circular running track where, as the sun fell, we witnessed a race using bicycles. There was some sort of substantial wager involved in the matter, as I recall, and the track had been closed off specially for the occasion. This was insufficient to prevent our ingress, obviously.

One of the competitors was wearing red, and the other blue. We never did discover their names. As the race started, red immediately pulled ahead. A few moments later, Holmes observed that if they maintained their pace, red would complete a lap in four minutes, whilst blue would complete one in seven.

Having made that pronouncement, he turned to me. ‘How long would it be before red passed blue if they kept those rates up, old chap?’

Whilst I wrestled with the answer, Holmes went back to watching the proceedings. Can you find the solution?”

Answer.

See the Track Problem for a solution.

A fun, relatively new, Sherlock Holmes puzzle book by Dr. Watson (aka Tim Dedopulos) has puzzles couched in terms of the Holmes-Watson banter. The following problem is a variation on the Sam Loyd Tandem Bicycle Puzzle.

“ ‘Here’s something mostly unrelated for you to chew over, my dear Watson. Say you and I have a single bicycle between us, and no other transport options save walking. We want to get the both of us to a location eighteen miles distant as swiftly as possible. If my walking speed is five miles per hour compared to your four, but for some reason—perhaps a bad ligament—my cycling speed is eight miles per hour compared to your ten. How would you get us simultaneously to our destination with maximum rapidity?’

‘A cab,’ I suggested.

‘Without cheating,’ Holmes replied, and went back to tossing his toast in the air.”

Answer.

See the Bicycle Problem for solutions.