Bob Ruyle

AB = AC ∠BAC = 80°, ∠CBD = 30°, ∠ADC = 150° Find the measure of ∠DAC. #mathpuzzle #Geometry #GeometricProblem

ABCD is a square with side length 10. Choose E so that AE = BE. Triangles BCE and FCE are congruent. Find the area of triangle ADF. #mathpuzzle #Geometry #GeometricProblem

@jamestanton @BradBMath The last table suggests a recurrence relation for f(N), where f(N) = no. of ways of splitting N coins into three nonempty piles.

@jamestanton Here's one possibility for an expression for the no. of ways to split N coins into three nonempty piles, (not counting order of piles). No proof given here. But, the idea is based on same reasoning as given by @BradBMath in puzzle of a couple days ago.

There is only 1 way to "split" a pile of N coins into one pile. There are N/2, rounded down to the nearest integer, ways to split them into two non-empty piles. (Order of the piles irrelevant.) Any structure of note for the counts for three-nonempty-pile splits?

Find the measure of ∠ADB. #mathpuzzle #Geometry #GeometricProblem

@BradBMath @jamestanton I think I followed your argument ... until the last bit where you calculated the value. I get this:

@jamestanton 49×50/2+18-3(18×19/2) = 730. So glad my answers matched. 🫤 I would like to get to the bottom of this, but I've exhausted my procrastimath time. Anybody see my mistake?

There are 50 ways to split 100 pennies into two non-empty piles: 1 & 99, 2 & 98, ..., 50 & 50. (Order of piles immaterial.) How many ways are there to split them into three non-empty piles?

AB = 7, AD = 2 ∠CBD = ∠DBA, ∠A = 2∠C Find BC. #mathpuzzle #Geometry #GeometricProblem

@asitnof @jamestanton Thank you! I got the idea only after reading your contribution.

@bruyle1 @jamestanton ¡Qué bonito! What an elegant solution, Bob! Thank you very much for sharing!

Looked at some old writings. Wondering how I came up with the numbers 4, 6, 12 to make this puzzle solvable. Hmm! What other values for speeds work for this puzzle? (3,5,15, yes!, 2,5,10, no!) [Assume the path is composed of clearly-defined uphill, downhill, and flat sections.]

Find the area of the shaded region. #mathpuzzle #Geometry #GeometricProblem

@MatildaSpicer Another way. Not necessarily a better way.

AB = 24, AC = 40, AD = 15 ∠BAD = ∠CAD Find CD. #mathpuzzle #Geometry #GeometricProblem

@ai_meh_s @TaghiBehradfar S1 : S2 = 1 : 1

Happy New Year S1 : S2=? Author: @TaghiBehradfar

α=?

Let A be the point of tangency of the tangent from B to the circle. Let the line through B intersect the circle at C and D. If ∠ABC=60°, ∠CAD=30°, and AB=2, find the radius of the circle. #mathpuzzle #Geometry #GeometricProblem

ABCDEF is a regular hexagon. Area[ABG] = 1, Area[CDEG] = 2 Find the area of the shaded region. #mathpuzzle #Geometry #GeometricProblem

A(ABC)=?