Puzzle 209
Triathlon - Round 1 - Logic Puzzles
During the latest round of the BrainBashers school triathlon the final results were mislaid, however, this is what we do know.
Hayden was fourth.
Alex was not the oldest but was older than Drew, who was not second.
The child who was next in age to the youngest, finished second.
The child who finished in third place was older than the child who finished first.
Billie was younger than the child who finished in third place.
Can you determine who finished where and place the children in order of age?
Puzzle Copyright © Kevin Stone
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Hint
Start by finding out who the oldest is.
Answer
# Name Age
#1 Drew youngest
#2 Billie next to youngest
#3 Alex next to oldest
#4 Hayden oldest
Reasoning
By (2), neither Alex nor Drew were the oldest. By (5), neither was Billie. Therefore, Hayden was the oldest, and by (1) came fourth.
#1
#2
#3
#4 Hayden oldest
By (4) the youngest didn't come third, and by (3) the youngest didn't come second. Therefore, the youngest came first.
#1 youngest
#2
#3
#4 Hayden oldest
By (3), the next to youngest came second, leaving the next to oldest in third.
#1 youngest
#2 next to youngest
#3 next to oldest
#4 Hayden oldest
By (2), Drew wasn't second, but Alex was older, so Drew can't be third either. Therefore, Drew can only have come in first.
#1 Drew youngest
#2 next to youngest
#3 next to oldest
#4 Hayden oldest
By (5) Billie didn't come third, so came second. Leaving Alex in third.
#1 Drew youngest
#2 Billie next to youngest
#3 Alex next to oldest
#4 Hayden oldest
Puzzle 210
During a recent trip to Scotland, I filled my car's 10 gallon fuel tank to the very top.
I travelled at 60 mph up the motorway, and I knew that I averaged exactly 40 miles per gallon.
However, the moment I started, my fuel tank developed a leak, and four hours later I came to a complete stop as I'd run out of fuel!
How much fuel did I lose through the leak?
Puzzle Copyright © Kevin Stone
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Hint
How far did I travel, and how much fuel did this use?
Answer
I had lost 4 gallons of fuel.
Reasoning
I travelled at 60mph for 4 hours, which is 240 miles.
At 40 miles per gallon this used 6 gallons, which meant the remaining 4 gallons were lost.
Puzzle 211
Using a 3 gallon container and a 7 gallon container (along with a water source and drain)…
…can you measure exactly 5 gallons in the fewest steps?
Puzzle Copyright © Kevin Stone
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Hint
Start by filling the 7 gallon container.
Answer
Here are the contents of the containers after each stage:
A B
0 7 fill B
3 4 fill A from B
0 4 empty A
3 1 fill A from B
0 1 empty A
1 0 fill A from B
1 7 fill B
3 5 fill A from B
This leaves 5 gallons in container B after 8 steps.
Puzzle 212
I have three daughters and each has one brother.
How many children do I have?
Puzzle Copyright © Kevin Stone
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Hint
I have fewer than 10 children.
Answer
4.
I have three daughters and one son.
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