At last year's BrainBashers snail race, 10 fine snails completed the tabletop course.
Predictably, as per every year, the results mysteriously went missing.
However, various spectators remembered the following snippets of information:
Orange Berry lost to Zebra Wings. Zebra Wings beat Orange Berry, Frog Flippers, and Apple Pie. Fizzy Pop lost to Minty Mouth, Orange Berry, and CD Player. Frog Flippers beat Windy Hill, CD Player, and Orange Berry. Top Hat lost to CD Player, Kipper Slippers, and Apple Pie. CD Player beat Top Hat, and Fizzy Pop. Apple Pie lost to Zebra Wings, and Orange Berry. Kipper Slippers lost to Apple Pie, and Frog Flippers. Frog Flippers beat Fizzy Pop, Minty Mouth, and CD Player. CD Player lost to Frog Flippers, Kipper Slippers, and Apple Pie. Top Hat beat Fizzy Pop, and Windy Hill. Minty Mouth lost to Windy Hill, and Orange Berry. Windy Hill lost to Apple Pie, and CD Player.
Can you work out who finished where?
Hint
Who finished first? Start with Clue 2, and then Clue 4.
Answer
Zebra Wings (ZW)
Frog Flippers (FF)
Orange Berry (OB)
Apple Pie (AP)
Kipper Slippers (KS)
CD Player (CP)
Top Hat (TH)
Windy Hill (WH)
Minty Mouth (MM)
Fizzy Pop (FP)
Reasoning
If we number the clues, write each name using two letters, and rewrite the clues so that those who finished ahead are written first:
ZW beat OB.ZW beat OB, FF, and AP.MM, OB, and CP, all beat FP.FF beat WH, CP, and OB.CP, KS, and AP, all beat TH.CP beat TH, and FP.ZW and OB both beat AP.AP and FF both beat KS.FF beat FP, MM, and CP.FF, KS, and AP, all beat CP.TH beat FP and WH.WH and OB both beat MM.AP and CP both beat WH.
By (2): ZW FF
By (4): ZW FF OB
By (7): ZW FF OB AP
By (8): ZW FF OB AP KS
By (10): ZW FF OB AP KS CP
By (5): ZW FF OB AP KS CP TH
By (11): ZW FF OB AP KS CP TH WH
By (12): ZW FF OB AP KS CP TH WH MM
By (3): ZW FF OB AP KS CP TH WH MM FP
After the local BrainBashers Horse Show, some friends were telling everyone who had won.
Unfortunately, the friends were having trouble remembering, and in the course of the afternoon, they changed their minds a number of times.
In summary, they made the following statements:
Andy said: Taylor Tripton won with Evening Sunrise. Alex Ambleton won with Morning Sunset. Frankie Flanton won with Evening Sunrise. Billie said: Sam Spinton won with Midday Night. Frankie Flanton won with Evening Sunrise. Taylor Tripton won with Morning Sunset. Chris said: Alex Ambleton won with Midday Night. Sam Spinton won with Midday Night. Sam Spinton won with Morning Sunset. Dale said: Alex Ambleton won with Evening Sunrise. Frankie Flanton won with Morning Sunset. Sam Spinton won with Midday Night.
However, none of the statements were fully true.
In fact, just six of the statements were exactly half true (either the person won, or the horse did), the rest were false.
Can you determine who won, and which horse they were showing?
Reasoning
Before we begin the reasoning, let's look at the hint: 'Could Alex Ambleton have won?'. There are three horses in the puzzle, and Alex Ambleton is stated to have won with all three of them. We know that none of the statements were fully true, so Alex couldn't have won otherwise one of the statements would have been fully true.
However, we don't need the hint to solve the puzzle.
By grouping the clues together, we have:
1. Frankie Flanton won with Morning Sunset.
2. Frankie Flanton won with Evening Sunrise.
3. Frankie Flanton won with Evening Sunrise.
4. Sam Spinton won with Midday Night.
5. Sam Spinton won with Midday Night.
6. Sam Spinton won with Midday Night.
7. Sam Spinton won with Morning Sunset.
8. Taylor Tripton won with Morning Sunset.
9. Taylor Tripton won with Evening Sunrise.
10. Alex Ambleton won with Midday Night.
11. Alex Ambleton won with Morning Sunset.
12. Alex Ambleton won with Evening Sunrise.
We know that none of these statements were fully true, so, we know that (for example) it wasn't Frankie Flanton with Morning Sunset.
We can create a grid of all the possibilities and place an X where we know that it can't have been that combination:
M-N
M-S
E-S
Frankie
X
X
Sam
X
X
Taylor
X
X
Alex
X
X
X
We now have an X for all but 3 possibilities, and we know that exactly 6 of the clues must be half true.
So …
… if it was Frankie Flanton with Midday Night then exactly 7 clues would be half true (clues 1, 2, 3, 4, 5, 6, 10).
… if it was Sam Spinton with Evening Sunrise then exactly 8 clues would be half true (clues 4, 5, 6, 7, 2, 3, 9, 12).
… if it was Taylor Tripton with Midday Night then exactly 6 clues would be half true (clues 8, 9, 4, 5, 6, 10), and this must be the correct answer.
?
Puzzle 4
Below you can find a proverb where the letters have been converted to their location in the alphabet, and spaces have been added.
