New answers tagged combinatorics
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Save now! All the digits at half the price
A bit messier than I'd like, but here goes.
As other answers have noted, the doubleable PD10 numbers we want are those where
Let's show that every such number can be specified by:
for an overall ...
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Save now! All the digits at half the price
Let's define some terms:
Now we can begin.
Let's break the problem down now.
Now for the final count!
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Save now! All the digits at half the price
My guess is:
First, observe that the first digit of $x$:
Then, the reasoning goes this way:
I'm not 100% sure of my calculus but this is how I did it:
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Clock hands at right angle
Here is a way I like to think about it
Where does your reasoning fall down
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How Many Magic Hexagons that use repeated digits?
Question 3 Is it possible to construct a Magic hexagon that uses repeated digits within the grid but doesn't have any repeated digits within any row columns or diagonal line?
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How Many Magic Hexagons that use repeated digits?
Question 1 How many unique patterns are there that use repeating consecutive digits?
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Twenty-four coins
Here's an algorithm that requires maximum 7 measurements (I believe):
Let's first set some terminology, note that each measurement of n coins can be one of 4 cases:
Case 0: All standard coins M = n.s
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What's the fewest weights you need to balance any weight from 1 to 40 pounds?
Once we have determined that the weights must be 1, 3, 9 and 27 grams, an obvious question to ask is how to use these weights to weigh an object.
One method, which is my candidate for most efficient, ...
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Twenty-four coins
An attempt to solve it with 7 measurements
Part 1 : possibility analysis
Part 2 : an (approximate) lower bound
Part 3: A strategy to (attempt to) get an actual solution with 7 measurements.
Part 4a ...
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Colour the positive integers without making a blue equation
How many?
Why (smaller cases)?
The working case:
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