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The bottom row are all identical to the baubles underneath.
The two below the 14 are a cube and a triangle that add up to 14.
Only possible values for the cube are 1 and 8
If 1 then the triangle is 13, which isn't a triangle number, so it must be 8 and 6
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The two on the bottom right are:
A triangle x
A square y
such that 8 + 2x + y = 23math hard; shopping
3 and 9This lets you fill in a bunch of them, up to the one above 23.
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Filling in all the above solutions, there's only one number left on the bottom row (left hand square) - call it Sl
This makes it fairly easy to work up to the two higher numbers and the higher square and triangle (Sh and T, respectively).
Sl + 6 + 14 + 25 + Sh 106 <=> Sl + Sh = 61Similarly (but not forgetting to add 48 twice):
Sl + T = 57The only pair of square numbers adding to 61 is 25 and 36
If Sl = 25 => T = 32
If Sl = 36 => T = 21
Since 21 is a triangle number and 32 is not, then:
Sl = 36, Sh = 25, and T = 21This makes the value of the star 433, if all my arithmetic is correct. The intermediate values are left as an exercise for the reader.
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@carrievs That's what I got.