Are these two partitions of the dots in a 4x4 grid compatible? (In each grid, the same coloured dots are in the same group)
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The largest set we considered yesterday is called the affine plane of order 3. Here’s a representation with each colour indicating a partition in the set. Find a different representation (different set of partitions) of the affine plane of order 3.
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Consider a set of pair-wise compatible partitions of the 9 dots. What’s the largest number of partitions that can be in this set?
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Let’s also call two partitions compatible if each group in one partition consists of a dot from each of the 3 groups in the other partition. How many partitions of the 9 dots are compatible with this one?
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Happy Monday! This week's problems are inspired by David Butler's post on bsky:
buff.ly/wzOUplR
Consider all the ways of splitting the following 9 dots into 3 groups of 3. Let’s call these partitions of the dots.
How many different partitions of the 9 dots are there?
Does the formula GCF(a, b) x LCM(a,b) = axb still work when a and b are fractions? What about the Euclidean Algorithm?
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Happy Monday! This week's problem is inspired by my idle musings. ^^"
If we were to extend the definition of factors to non-integers, which of the following would you say is a factor of 2/5: 2? 5? 1/5? 1/10? 2/15?
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If we place 4 points on the perimeter of a unit square and add up all pair-wise distances between them, what’s the biggest sum we can get?
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If we place n points on the circumference of a unit circle and add up all pair-wise distances between them, what’s the biggest sum we can get?
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If we place 4 points on the circumference of a unit circle and add up all pair-wise distances between them, what’s the biggest sum we can get?
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If we place n points on a line segment of length 1 and add up all pair-wise distances between them, what’s the biggest sum we can get?
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If we place 4 points on a line segment of length 1 and add up all pair-wise distances between them, what’s the biggest sum we can get?
#math#maths #ProblemSolving#iteachmath#mathsky
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