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

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?

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?

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?

011 - Calendar of Cubes

Hillary Black, a consultant horologist working in the city of Serendipity, is fascinated by calendars and likes to use unusual ways of displaying the date.

When it comes to showing what day of the month it is, she uses a pair of custom-made cubes.

Each morning Hillary moves these cubes so that the front faces of the cube show the current day of the month. The format is always two digits, with the first day of the month being 01, all the way through to the month's end, so that the seventh day of the month would be shown as 07, and the twenty fifth 25.

How are the cubes marked so as to allow Hillary to use them this way?