Colin James Physics - Logic puzzles.
Last updated: 25th June 2013.
Logic puzzles.
These are general logic puzzles - not Physics puzzles, but they should be challenging and fun (just like Physics).
If you know what you are looking for in a puzzle or have done a similar one before you may find an easier puzzle harder or a harder one straightforward.
So it its worth scanning through the different categories.
When you click on a puzzle it will appear below (and the screen will move down to show the puzzle) with a solution further down the screen.
Easier puzzles.
Running puzzle.
Tennis puzzle.
Water puzzle.
Walking puzzle.
Harder puzzles.
Spending puzzle.
Cakes puzzle.
Ages puzzle.
Chess puzzles.
Chess puzzle 1.
Chess puzzle 2.
Chess puzzle 3.
Chess puzzle 4.
Chess puzzle 5.
Walking puzzle.
There are two people walking together and they walk at the same speed.
Shortstride takes three strides for every two that Longstride takes.
They both start off with their left feet on the ground and lead off with their right feet. Their feet only touch the ground briefly as each step is taken (they don't shuffle).
The problem is 'How far do they have to go before both right feet touch the ground at the same time?
Solution
Solution
Solution
Solution
Solution: Walking puzzle.
If you couldn't find a solution - well done, you have solved it. Sorry to give you a trick question.
There is no solution to this problem in that the right feet are never synchronised to touch the ground at the same time.
The interesting bit is to find out why.
Take the steps of Longstride to be the standard and say they start at zero for the left foot staying on the ground.
Longstride: 0 (left) 1(right) 2(left) 3(right) and so on ...
Shortstride: 0 (left) 2/3(right) 4/3(left) 6/3(right) 8/3(left) 10/3(right) and so on ... which is the same as:
Shortstride: 0 (left) 2/3(right) 1 1/3(left) 2(right) and so on ...
You can see that after 4 of Longstride's paces we are back with Left and Left for both walkers.
In terms of numbers we are looking at 1, 3, 5 ... (3/3, 9/3, 15/3 ...) for Longstride's right foot on the ground; and
Shortstride's right foot on the ground at 2/3, 6/3, 10/3 ...
The odd numerators (3, 9, 15 ...) in Longstride's right foot on the ground pattern; and
the even numerators (2, 6, 10 ...) in Shortstride's right foot on the ground pattern prevent both people's right feet on the ground at the same time being synchronised.
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