Lies, Boolean logic and crime scenes: Chapter One

24 Oct 2016

Detective George 'Logic' Boole. Image: JRP Studio/Shutterstock

Logic is an integral aspect of mathematical thinking. But can you use logic to help solve this very real fictional crime?

A spark lights up the darkness, momentarily illuminating a craggy, weathered face.

This face has seen things. Done things. This face, and the body to which it is attached, has worked 30 long years on the force – 30 long years of blood and of misery, of bad coffee and even worse relationships.

But this face sees light at the end of the tunnel. This face sees its retirement creeping closer.

In this moment, however, lying between this face and retirement are three bodies.

The face takes a long draw on its cigarette as it ponders the scene before it. This isn’t the face’s first crime scene. Far from it. But this one seems special somehow.

Engrossed in the gruesome spectacle, it takes a while for the face to become aware of the fact that someone is trying to get its attention.

“Uhm… Detective? Detective Boole? … George?”

“What is it, officer?” snaps Boole.

“We’ve got some suspects for you, sir. Back at the precinct.”

“Fine. You’re driving.”

Boole is no stranger to interrogation. You could say he was made for it. Straight out of the academy, he took to it like a duck to… well, you know. ‘One of the finest logical minds of our time. Maybe any time.’ That’s what his captain had said.

Boole made sure to put that logic to good use. He had almost as many arrest records to his name as he had enemies, and that’s just if you count the ones within the force. He might be a hotshot detective, but that doesn’t mean he’s any good at not rubbing people up the wrong way.

“Where are they, officer?” growls Boole. The young officer – O’Grady, Boole thinks his name is – flinches before answering.

“We’ve got them in your usual rooms, sir.”

The hard-bitten exterior Boole has built up over the years works wonders when it comes to interrogating suspects. Some crack the second he snarls his first question. Most hold out for a while, but cave when he starts to get in their faces.

Others are tougher nuts to crack. The five rounded up this evening are definitely of that variety – none of them are willing to land themselves in it, and they all came prepared.

But none of them were prepared for Boole.

The detective takes five minutes with each suspect. That’s all he needs to figure out that one of them is lying about when they arrived at the scene. But which one?

Those 30 years are beginning to take their toll. His mind is still sharp, but it’s starting to take longer than it used to for Boole to get everything neatly lined up and squared away.

He sits, poring over the perps’ testimonies, trying to find the lie that he feels but can’t see just yet.

Suspect 1 [Alonzo]: “I arrived first.”

Suspect 2 [Baz]: “I arrived second.”

Suspect 3 [Carl]: “I arrived third.”

Suspect 4 [Darnell]: “Alonzo and Baz, right? One arrived before me, one after me.”

Suspect 5 [Eric]: “Baz and Carl? One got there before me, the other got there after.”

Boole may be old, but his logic hasn’t failed him yet. As he stares at the interview transcripts, the shadow of the truth begins to emerge – and the shadow of the lie.

“I’ve got him,” mutters Boole. “I’ve got him.”

Who has Detective Boole got? Who’s lying? And what order did the suspects really arrive in?

Scroll down for the solution to this week’s puzzle.

maths puzzle crime


Boole pulls out a stool and sits down at the interrogation table. He’s been on the job too long to waste any time beating around the bush. Raising his eyes, he locks his steely gaze on his perp.

“Give it up, Bas. It’s over. We’ve got you.”

Of course, Bas doesn’t go quietly.

In the face of his protestations of innocence, his reams of ‘but I couldn’t haves’ and ‘I wouldn’t hurt anyones’, Boole stays calm and silent. Over the years, he’s learned that’s the best way to get the confession. Just let them talk themselves out.

When Bas finally runs out of steam, Boole explains in great detail why there’s no point in arguing. He explains that Bas hung himself – so to speak – the second he opened his mouth.

Boole tells Bas about how he worked it all out, sitting at his desk with the five accounts spread before him.

“See, you, Alonzo and Darnell couldn’t all be telling the truth. Neither could you, Carl and Eric. Your statements contradicted each other. There was a lie buried in there somewhere, and you were the common denominator.

“It wasn’t hard to do the maths. Once I figured out that you were the killer, the rest fell into place. I knew everyone else was telling the truth. Alonzo got there first, then Darnell arrived, then Carl, then Eric. You followed them in, circling back to check out your crime scene so no one would suspect you.

“It didn’t work.”

As the officers haul Bas away in cuffs, Detective George Boole returns to his desk, to sit and wait for the next call.

He’s one case closer to retirement.

This week’s maths puzzle was part of the first round of the Dutch Mathematics Olympiad. Secondary school students in Ireland who wish to participate in Olympiads are encouraged to attend free Mathematics Enrichment Programmes organised as part of the Irish Mathematical Olympiad.

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Kirsty Tobin was careers editor at Silicon Republic