026 - Rashomon

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025 - Blowout

Farmer Joe has 15 four-hour candles.

At 7 pm, Farmer Joe lights all his candles.

At 9 pm, he extinguishes one third of them.

At 10 pm, a breeze blows out half of those still burning.

At 11 pm, how many candles does Farmer Joe have left?

024 - Ave Caesar

"Are these all of them?" asked Detective Dockland.

"Yes," replied Hillary Black. "I've given you a copy of every other document in the safe on the night of the robbery. I should warn you, though, they're all encrypted."

Dockland glanced briefly at the top document in the stack. "I don't think much of your idea of encryption."

"Oh, that one's not serious encryption. She just does them that way for fun," said Hillary.

Dockland paused, and looked at the document longer, before adding, "She's right, in that the math problem is't very hard either."

What is the answer to the math problem Dockland is referring to? The document reads, in full:

DY RSVVKBI

GYBU MYXDSXEOC. CY PKB KVV DOCDC YX DRO NOFSMO RKFO ZBYFON XOQKDSFO. GO KBO CDSVV RYZOPEV YP MBKMUSXQ DRO KMDSFKDSYX COAEOXMO GSDRSX DRO XOHD GOOU. DRO DOKW SC ECSXQ LBEDO PYBMO LED S CDSVV DRSXU DROBO WECD LO KX OKCSOB GKI. SD'C VSUO PSXNSXQ DRO CEW YP KVV ZYCSDSFO SXDOQOBC LODGOOX YXO KXN YXO REXNBON SXMVECSFO - DROBO SC XY XOON PYB DONSYEC KNNSDSYX GROX IYE UXYG DRO CRYBDMED. KXIGKI S RYZO DY RKFO WYBO XOGC XOHD DEOCNKI.

LOCD BOQKBNC

TKMUS

023 - Bookworm

A bookworm has made its way into the Serendipity Municipal Library, and set its sights on the ten-volume Journals of Abernathy Gould, which are organised in numerical order, cover to cover, on one of the Library's lower shelves.

Each volume of the journals has 1,000 pages. If the bookworm starts eating at page 1 of volume 1, and finishes at page 1000 of volume 10, how many pages will it have eaten through?

022 - Movie Business

Anwar Patel has another challenge for his students.

"In the history of cinema, our filmmakers have created a great many fictional characters. But not all characters are human; over the years we've seen a wealth of memorable corporations brought to the screen. Can you name the movies that these fictional corporations appeared in?"

1) LesterCorp
2) Tyrell Corporation
3) Initech
4) Weyland-Yutani Corporation
5) Jackson Steinem & Co
6) Rekall
7) Cyberdyne Systems Corporation
8) Monumental Pictures
9) Omni Consumer Products
10) Hudsucker Industries

021 - Jigsaw

How many?  (Less than ten.)

020 - Equal Opportunities

Detective Kent Dockland is questioning Hillary Black about the recent break-in at her offices.

"Can you tell me a little bit about your business?" he enquires.

"We're a consulting firm," says Hillary. "We mostly do work for Logidyne Labs, a research and development company."

"And how many people are employed here?" asks Kent.

"Well, each male worker has one fewer female co-worker than he does male co-worker," says Hillary, "and each female worker has two male co-workers fewer than twice the number of her female co-workers."

"Thank you, ma'am," says Kent. "That's very helpful."

How many people are employed at Hillary's consulting firm?

019 - Age Detective

Responding to an urgent call, Detective Kent Dockland attends the offices of Hillary Black, where a burglary has been reported.

Hillary, though, is unimpressed. "Dockland?" she says. "I've heard you've got a bad reputation on the police force. Why shouldn't I send you back and request a good detective?"

"I am a good detective, ma'am,' says Dockland.

"Well, then," says Hillary, "tell me this: how old are my daughters?"

"How many daughters do you have?" asks Dockland.

"Three," says Hillary. "The product of their ages is 36, and the sum of their ages is the same as the number on my ID badge."

Dockland looks at Hillary's ID badge. "I'm sorry, ma'am," he says. "I can't tell you the answer to that question given that information."

"Oh, of course you can't!" says Hillary. "My apologies. I should have added that when I went into labor with my youngest daughter, both of her sisters were running around the back yard."

"Well, then, that's easy," says Dockland, and tells her the answer.

"Well, Detective, it seems I've been mistaken about you," says Hillary. "Let me tell you about these documents that were stolen..."

How old are Hillary's daughters?

018 - Happy Families

Anwar Patel is Professor of Media at the Serendipity University. He set the following challenge for his students.

"Television has given us a rich history of characters bound by family ties. For each of the families below, can you provide their surname and the television show they come from?"

1) Gomez, Morticia, Pugsley, Wednesday, Fester
2) Ross, Monica, Jack, Judy
3) Willie, Kate, Lynn, Brian
4) Dick, Sally, Harry, Tommy
5) Chris, Meg, Lois, Peter, Stewie
6) Nick, Tony, Joey, Blossom
7) Marcia, Carol, Greg, Jan, Peter, Cindy, Mike, Bobby
8) Danny, D.J., Stephanie, Michelle

017 - Pork Grill

Tired of complicated inter-jurisdictional swinekeeping legislation, Farmer Joe has converted his pig farm into a restaurant. Farmer Joe's BBQ Porkatorium is now the premier pig-themed eatery in Oddsville.

Farmer Joe's secret is his ability to cook pork chops in record time, despite the tiny size of the kitchen's pork grill.

The pork chops used in Joe's delicious Porkgasm Surprise need to be grilled for 10 minutes on one side, and then 10 minutes on the other. The pork grill can only hold two chops at once.

Nevertheless, when three customers simultaneously order the Porkgasm Surprise, Joe is able to prepare it surprisingly quickly. What is the fastest time in which Joe can complete the grilling of three pork chops on his pork grill?

016 - Brevity of Communication

Kent Dockland doesn't get on well with his co-workers at the Serendipity Police Department. Today, as he's trying to finish some incident reports on his computer, he's distracted by his co-workers loudly discussing the comparitive merits of cars, motorcycles, and speedboats.

Peter Bernard, the loudest, meanest cop on the force, spots Kent at his computer. "Hey Kent!" he yells. "What kind of vehicle do YOU like?

"Here's the thing, Peter," says Kent. "This isn't news. You understandably really like cars or motorcycles. But I have to finish this incident report, it's due today, and you and your idiot friends aren't helping."

Peter scowls. "Don't be a loser, Kent. The report can wait five minutes. What's your vehicle of choice?"

Kent stares at Peter, and says, "I just told you."

What is Kent's favourite kind of vehicle?

015 - Shifty Triangle

Documents have been stolen from Hillary Black's safe! Or have they?

Hillary has opened her safe this morning to find that her crucial documents have been moved around. At first she was sure there were some missing, but now she's not certain.

Always a stickler for patterns, Hillary kept her oddly-shaped documents arranged in the shape of a triangle. And indeed, they're still in the shape of a triangle.

The current shape of the documents is triangle A in the attached image.
Yesterday, Hillary had the documents arranged as triangle B.

The purple square document appears to have vanished, but the triangles look the same.

Has anything actually been removed? And if so, what's the explanation for the similarity of the triangles?

014 - Logidyne Hats

Logidyne Labs, a research and development company based in the city of Serendipity, is welcoming its newest round of recruits today. Before they can start work, Logidyne's head researcher Jacki Renquist subjects the three recruits to an unusual test.

Jacki instructs the three recruits to be seated, and then places a hat on the head of each recruit, such that each recruit can see all of the other hats, but none of them can see their own.

"Each hat is either white or blue," says Jacki. "There is at least one blue hat. You may not talk amongst yourselves, or communicate in any way. You may not remove your hat, or otherwise view its colour. None of you may start work until one of you correctly declares the colour of your own hat. If any of you incorrectly guess the colour of your hat, you will all three be fired. You have all been hired on the basis of your perfect command of rational thought, and therefore I am sure you will be able to start work today."

Jacki was correct and the recruits started work shortly thereafter.

How did they solve the test?

013 - Jason D

Hillary Black keeps her most valuable secrets in a locked safe. Unlocking the safe requires a 12-letter-long passcode.

Unfortunately Hillary isn't good about keeping her passcode secret. She wrote it on a piece of paper, and then dropped the paper outside her office, where it's been trodden on and damaged. A lucky burglar has found the scrap of paper and is now trying to make sense of it.

The first six letters of the code are illegible, but the last six are:

J A S O N D

What is the complete code likely to be?