# Twelve Labours - #04 Erymanthian Bar

This puzzle is part of the ‘Twelve Labours’ series. Previous instalments can be found here: Prologue | 01 | 02 | 03

Now one crate lighter, Hercules made his way back up the road to the Erymanthian Bar. Outside, a chalkboard proclaimed the sporting fixtures for the coming week that would be shown live on television. Football, tennis, athletics, rugby... All the weekend’s horse racing too. Hercules smiled to himself – the owner, Pholus, was an old friend of the family, and completely mad about all things sports... especially when it came to horses.

“Of course, I used to jockey all over the country when I was younger – before the accident, I mean...” Pholus chatted away amicably, as Hercules unloaded his trolley. For once, Hercules did not begrudge the task he had been set – helping out Pholus (who always managed to remain cheerful despite his crutches) seemed like a good thing to do. “These days I’m lucky if I can manage a hole or two at the golf course up the road. But I’m happy, you know – I run a sports bar, I’ve got good, strong wine, and plenty of custom; really, I couldn’t ask for any more. I’m over the moon.”

Pholus gestured around his establishment, and Hercules had to agree it was truly a wonderful sight. Every wall was covered in sporting paraphernalia – scarves, signed photographs, souvenir programmes, banners... At the end of the bar was the dartboard where Hercules had scored his first ever one-eighty maximum; beyond that stood the table football, at which Hercules’ father had regularly contrived to lose to his young son; and just beyond that stood the snooker table that conjured up memories of the sound of chalk, the feel of a cue sticky with stale beer, and the smell of cigarette smoke that always seemed so illicit.

“Oh, let me help you set that up,” said Hercules, spotting the messy snooker balls. But on approaching the table, he stopped short. The green felt was covered in letters. Hercules laughed and shook his head – clearly, even his friend Pholus had sided with his mother and was testing him today!

Greyscale version available at page end...

“What does my mum need from you?” Hercules sighed, one eyebrow raised. Pholus laughed.

“Just something for the house. It’s a bit heavy though – I recommend you keep hold of that flatbed trolley...” Pholus handed Hercules a cue. “You’ve got one shot to work it out – it has to be a legal one, of course.”

TASK: Find the legal shot which will help Hercules deduce the item in Pholus’ possession. To be awarded the green checkmark, a complete answer must include an explanatory diagram.

HINT 1 (23-Oct-19):

The solution requires only one ball to be hit head-on by the cue ball (no tricky angles of impact). Once hit, the target ball does not touch any other ball on the table on its way to a pocket (although at one point it looks like it comes really really close to one...). It may help to assume a 'point mass' when drawing the balls' bounce...

HINT 2 (25-Oct-19):

As has already been discovered, a hidden message in the puzzle reads "YOU WON'T SOLVE THIS BY SHOOTING DIRECT." In fact, balls involved in the correct shot will hit the cushions 4 times in total. It is important to note that a ball hitting a cushion will always move away from it at a particular calculable angle - think symmetry...

HINT 3 (27-Oct-19):

The answer you seek is a 9-letter compound word. One letter appears within it 3 times; the others are all unique. There are no leading articles.

The same image is reproduced below in greyscale, for puzzlers with colour-blindness. The white cue ball is a numberless grey ring; each colour ball is a grey ring marked with its points value; each red ball is a fully shaded grey circle:

• Found one of the red herrings: rot13(Vs lbh ernq gur yrggref orgjrra gur phr naq gur erq onyyf, fgnegvat jvgu gur bar tbvat gbjneqf gur hccre evtug cbpxrg, lbh trg "Lbh jba'g fbyir guvf ol fubbgvat qverpg") – Darrel Hoffman Oct 22 at 17:11
• Nice spot @DarrelHoffman - that should prove useful... – Stiv Oct 22 at 17:15
• I've been trying this for a while, but haven't been able to get anywhere. For more complicated shots, it seems impossible to judge the actual angles, and I've had several attempts that seem to be spelling some fragment of a message, but after a few bounces they go nowhere. (And it seems to me that in the two messages I have found, the letters aren't perfectly aligned, so I can't even rely on that to help confirm whether a path is correct. Like, the K left of the bottom middle pocket should be higher up - it's not even on my path though, unless I bounce halfway inside the edge.) – Deusovi Oct 23 at 2:31
• @Deusovi On the correct path all letters should be pretty much perfectly aligned... As a practical tip I created this puzzle just in Microsoft Word. In that program (and similar) it's possible to draw a line then draw a perfect reflection of that line by dragging one end over the other and then matching the dimensions of the first. You can then alter the length by dragging one end and holding Shift, retaining the angle. This might help with judging angles. (You may know this already but not everyone might...) – Stiv Oct 23 at 6:20
• V xrrc gelvat gb genpr onpx sebz n cbpxrg naq znxr ersyrpgrq obhaprf hagvy V trg onpx gb gur phr onyy. Unira'g sbhaq gur pbeerpg natyr lrg ohg V'z fhfcrpgvat gur raq vf gur hccre evtug cbpxrg onfrq bss bs abguvat fhofgnagvny. V srry yvxr V'z trggvat pybfr ohg nyfb gung V unir fgnegrq ergelvat snvyvat nafjref. V'z whfg hfvat gur "Syvc Ubevmbagny" srngher va zfcnvag naq pbcl/cnfgvat gur yvar – Poke Oct 25 at 4:34

WOODSTOVE

The diagram below shows the path of the shot. The diagram is made from flipping and inverting the snooker table at boundaries such that all paths would be straight lines.

Here is the path on the table by itself

• Perfect! Well done Jens! And what an interesting way to demonstrate the answer. Thanks for solving :) +1 and a green checkmark for you... – Stiv Oct 27 at 7:09
• Thanks! The first diagram is actually the way I solved the problem. Your second hint was the biggest help as it reduced the possible paths I had to test to around $60$. Nice puzzle! – Jens Oct 27 at 12:57
• Wow, what an inspired way to solve it - it had never crossed my mind that someone might try and solve it with this method! Makes perfect sense though. Thanks and well done again! – Stiv Oct 27 at 13:38

A YOGA MAT

With the correct shot

requiring some right English, as shown here:

Oh, a quick note about part of the shot:

When you give the cue ball right English, it will continue to have right English, but when it hits an object ball, it will impart left English on the object ball. The spin and friction of the cue ball cause the object to rotate in the other direction. That's why the red comes off the top cushion with left spin.

And here are some wrong answers:

As mentioned in the comments, the red balls in clockwise order read YOU WONT SOLVE THIS BY SHOOTING DIRECT:

And I found a few more: PINK IN WAY, BLOCK, BLACK SUNK, SHAME, and WIDE:

If anyone has more, I'm happy to add them!

• Nice find. Was this just trial and error? – Poke Oct 23 at 3:15
• For the most part. I looked for collinear letters that could be part of a word and then followed them back to the cue ball. – hdsdv Oct 23 at 3:17
• Wow! This is very creative hdsdv but this item wouldn't be heavy enough for Hercules to need the flatbed trolley... I probably wouldn't describe this as something 'for the house' either. In fact the solution is much simpler than this one! I'll add a hint later today to help people narrow down their options. +1 for a sterling effort :) (@Deusovi, note these comments also) – Stiv Oct 23 at 6:05
• I'd also say your path includes a few extra letters. The true path uses every letter it passes directly through... – Stiv Oct 23 at 6:08
• Thanks for the kind words :) I was sure I had found it! As an aside, I really enjoy this series so far. I'm excited to see where it goes. – hdsdv Oct 23 at 8:39