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# Who's keeping score?

## Question

When four friends, Bill, Ed, Jim and Tom, began their foursome at Fairview Links last Saturday, they discovered to their dismay that no one had brought a pencil to keep their scores. And well let's just say that in the clubhouse afterward there was some confusion. Here are four "facts" that each player remembered. But fair warning, it turns out only two of each group of statements are true. And, if it helps, they all correctly remembered that no two players had the same final score.

• Bill:
I beat Jim and Tom.
Ed shot 111.
Jim took 6 on the last hole.
None of us broke 100.

• Ed:
Bill wasn't last.
I was the winner.
Jim finally broke 100.
I shot 98.

• Jim:
I beat Bill and Ed.
The last hole was not my best.
We didn't all break 100.
Tom wasn't the winner.

• Tom:
Ed beat Bill.
I was the winner.
Bill placed between Ed and Jim.
The last hole was Jim's best.

That's it. But surely by now you know what order they actually placed.

## Recommended Posts

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Spoiler

Assuming "X beat Y and Z" allows X to beat Y but lose to Z.

Ed, Jim, Bill, Tom

Ed:
Bill wasn't last.

I was the winner.
Jim finally broke 100.
I shot 98.

Jim:
I beat Bill
﻿and Ed.
The last hole was not my best.

We didn't all break 100.
Tom wasn't the winner.

Bill:
I beat Jim and Tom.
Ed shot 111.
Jim took 6 on the last hole.
None of us broke 100.

Tom:
Ed beat Bill.
I was the winner.
Bill placed between Ed and Jim.

The last hole was Jim's best.

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A couple assumptions:

"We﻿﻿ didn't all break 100﻿.﻿" includes the possibility that no one did.

"Bill﻿ placed between﻿ Ed and Jim" means directly between.

Ed, Bill Tom, Jim

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Didn’t all break ... just rules out the case that all broke ... anything else is possible

Between Ed and Jim means beat one and lost to the other.

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On 6/24/2019 at 1:15 AM, Thalia said:

A couple assumptions:

"We﻿﻿ didn't all break 100﻿.﻿" includes the possibility that no one did.

"Bill﻿ placed between﻿ Ed and Jim" means directly between.

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Does this solution imply that

Spoiler

Jim's statement 2 and Tom's statement 4 are both false?

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Spoiler

Ed:
Bill wasn't last.
I was the winner.
Jim finally broke 100.
I shot 98.

Bill:
I beat Jim and Tom.
Ed shot 111.
Jim took 6 on the last hole.

None of us broke 100.

Tom:
Ed beat Bill.
I was the winner.
Bill placed between Ed and Jim.

The last hole was Jim's best.

Jim:
I beat Bill and Ed.
The last hole was not my best.

We didn't all break 100.
Tom wasn't the winner.

With the previous assumption about the meaning of between.

Edited by Thalia

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