Mathematical Puzzle

Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 18 MPH between the 2 friends until the friends meet.
How many miles does the pigeon travel?
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Below the four parts have been reorganized. The four partitions are exactly the same in both arrangements. Why is there a hole?
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Both triangles are made of identical parts. In the bottom one is one empty square though. How is it possible?
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A frog is at the bottom of a 30 meter well. Each day he summons enough energy for one 3 meter leap up the well. Exhausted, he then hangs there for the rest of the day. At night, while he is asleep, he slips 2 meters backwards. How many days does it take him to escape from the well?
Note: Assume after the first leap that his hind legs are exactly three meters up the well. His hind legs must clear the well for him to escape.
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There are twenty coins sitting on the table, ten are currently heads and tens are currently tails. You are sitting at the table with a blindfold and gloves on. You are able to feel where the coins are, but are unable to see or feel if they heads or tails. You must create two sets of coins. Each set must have the same number of heads and tails as the other group. You can only move or flip the coins, you are unable to determine their current state. How do you create two even groups of coins with the same number of heads and tails in each group?
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You have infinite supply of water. You also have 5 quart and 3 quart buckets. What is the least number of steps you will require to measure precisely 4 quarts?
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Two observations were made of a clock at different time:
1st observation:
The hour hand is exactly at a minute mark and the minute hand is six minutes ahead of it.2nd observation:
The hour hand is exactly on a dissimilar minute mark and the minute hand is seven minutes ahead of it.Can you find out how much time has passed between the above two observations?
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The number of hours left today is half of the number of hours already passed. What time is it?
A. 8:00 a.m.
B. 12:00
C. 14:00
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After the recent Puzzle annual marathon, the judges were comparing notes to determine who finished where. From their notes, can you help them to reconstruct the final result?
 Matthew Merryman beat Tom Trent and Jimmy James.
 Peter Piper beat Jimmy James, Tom Trent and Alan Ardman.
 Zach Zebra lost to Peter Piper.
 Graham Goodfellow beat Tom Trent
 Zach Zebra beat Frank Flintbone.
 Graham Goodfellow lost to Frank Flintbone and Peter Piper.
 Tom Trent beat Brian Brick.
 Alan Ardman beat Zach Zebra, Kevin Kingfisher and Graham Goodfellow.
 Kevin Kingfisher lost to Graham Goodfellow and Matthew Merryman.
 Brian Brick beat Kevin Kingfisher.
 Matthew Merryman lost to Alan Ardman and Zach Zebra.
 Frank Flintbone beat Tom Trent, Matthew Merryman and Brian Brick.
 Tom Trent lost to Jimmy James and Alan Ardman.
 Jimmy James beat Graham Goodfellow and Brian Brick.
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At the recent spring fete, four keen gardeners were displaying their fine roses.
In total there were four colours and each rose appeared in two colours.
From the clues below can you tell who had which colour roses?
 Mr Green had a yellow rose.
 Mr Yellow did not have a red one.
 Mr Red had a blue rose but not a green one.
 Mr Blue did not have a yellow one.
 One person with a red rose also had a green one.
 One person with a yellow rose also had a blue one.
 One of the persons with a green rose had no red.
 Neither of the persons with a yellow rose had a green one.
 No person has two roses of the same colour.
 No two persons had the same two colour roses and their names provide no clues.
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