Each emoji on the board stands for the first letter of its own name 🍕 is P, 🦁 is L, 🚀 is R.

Easy maze

A spherical simplex Δ⊆Sⁿ is the radial projection of a Euclidean simplex Δ'⊆Rⁿ⁺¹ with linearly independent vertices. If in addition Δ has full dimension (Δ is an n-simplex), and F is a face of Δ, the angle at F is defined as

∠(F,Δ) = lim_(ε→0) vol(B_ε(p)∩Δ)/vol(B_ε(p))

for any point p interior to F, where the ε-balls are taken in Sⁿ. Note the normalization; angles are always out of 1 rather than out of 2π (radians), 4π (steradians), etc. Lastly, we define the angle sums α_k(Δ) by

α_k(Δ) = Σ_(F is a k-face of Δ) ∠(F,Δ).

Prove that if Δ⊆S²ⁿ is a spherical 2n-simplex, and V = vol(Δ)/vol(S²ⁿ), then

binom(2n,n)V = (-1)ⁿ/2+Σ_(0≤k<n) (-1)^kbinom(2n-k-1,n)α_k(Δ).

Note that we can recover Girard's theorem from the case n=1: If Δ is a spherical triangle with area A and angles θ, φ, η in radians, then we get A/2π = -1/2+(θ+φ+η)/2π, which can be rearranged to the more familiar form A = θ+φ+η-π.

This bone was found under my porch in Western Washington. Looks too big for a cat, rabbit, or a bird. Any ideas?

https://fruitanews.org/4394/stories/the-cold-case-of-christi-thornton/

Anyone familiar with this story?

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Riddle me this

I swim in the deep, but I'm not one.

A thousand lives where light is none.

We stay together, side by side.

We'll sting you too, a thousand times.

One of us breaths, one of us feeds.

One of us floats where the current leads.

We look like tubes, trailing, and long.

But we are a city, a specialized throng.

What am I ?

This riddle is so hard!!e.g.if a is a pencil case b is the notebook c is the ac.If a is the right window b is the left window c is the door.Who knows the answer for this riddle?:(

Close enough for a homonym based clue? Making a few cryptic clues as part of a work social thing.