Great challenge!! Math facts: SUM(SEQUENCE(n)^3)=SUM(SEQUENCE(n))^2 for any "n" for n=9 1+2+3+4+5+6+7+8+9=45 or SUM(SEQUENCE(9))=45 and 45^2=2025 Because of 9 , my idea went somehow to SUDOKU games, the coolest and most popular puzzle game related with first 9 nr. This can be a challenge, Creating and/or Solving an array of 5x5 SUDOKUs. It's a little bit more complicated than inventing random patterns, so if you like the idea let me know. It will reflect the real power of what Excel can do these days with simple formulas/functions to solve such a popular game.
Excellent - I saw this elsewhere. 1 cubed + 2 cubed + ... 9 cubed is very impressive. They also had (20+25)^2 = 2025 and a comment added had 1^0 + 2^0 + ... + 2025^0
I tried a bunch of things, and here is my final approach: I applied a three-color scale to my grid using a dark green for both the lowest and highest values, and a lighter green for the 45% percentile. I used the Excel logo colors, hexacodes 185B37 for dark green and 3C381 for light green. With that set up, what I wanted to do next is to use a formula to return zeros for all the numbers that have a square component. In other words, if either the row or the column is a square number it returns a zero, otherwise a one. That would be this formula: =ROUNDUP(MOD(SQRT(MAKEARRAY(45,45,LAMBDA(X,L,X*L))),1),0) but I didn't like the image it created, so I multiplied the array with itself before taking the mod. =ROUNDUP(MOD(SQRT(MAKEARRAY(45,45,LAMBDA(X,L,X*L)))*SQRT(MAKEARRAY(45,45,LAMBDA(X,L,X*L))),1),0) I am not sure what it is doing but it will work. I gave that formula a defined name: "Buy_the_Book" I then created this elegant formula: =MAKEARRAY(45,45,LAMBDA(X,L,POWER(X,L)))*Buy_the_Book The result is a quasi-random pattern that looks like a maze. But it is not random; it is symmetrical! I liked it. It also looks like a QR code, which would be really neat. You can also take out the Buy_the_Book portion and get a new arching visual that is kind of neat.
You could implement Conway’s Game of Life or Langton’s Ant on a 45x45 grid starting from some simple pattern (like a big XL), and see if it comes up with an interesting pattern… it wouldn’t be easy to do in one formula, although these days everything is possible!
First comment. Happy new year sir. I would like to see a tutorial about how can you provide 6 random numbers that has a range form 1-42 in excel. Providing it, is much appreciated 🙏🤍
Here's the formula (sorry it's not formatted, YT keeps deleting it so had to make do it Bo style!) =LET(xleft,-1.98,xright,-1.4,ytop,-0.1,ybottom,0,size,45,iterations,10,fnMandelbrot,LAMBDA(xleft,xright,ytop,ybottom,size,iterations,MAKEARRAY(size,size,LAMBDA(c,r,LET(x_0,xleft+(r-1)*(xright-xleft)/size,y_0,ytop+(c-1)*(ybottom-ytop)/size,fn,LAMBDA(ixy,iteration,LET(i,INDEX(ixy,,1),x,INDEX(ixy,,2),y,INDEX(ixy,,3),repeat,AND((x*x+y*y)=iteration-1),newi,IF(repeat,iteration,IF(i
Here are some of my ways to have gradient. I am just going to use One Cell Formula with MAKEARRAY 1. Radial Gradient (Circular) =MAKEARRAY(45, 45, LAMBDA(r,c, SQRT(r^2 + c^2))) 2. Center-Radial Gradient =MAKEARRAY(45, 45, LAMBDA(r, c, SQRT((r-22)^2 + (c-22)^2))) 3. Wave Gradient (Sine Wave) You can actually play wit the 22.5 here and it will be pretty amazing =MAKEARRAY(45, 45, LAMBDA(r,c, SIN(r/22.5) + COS(c/22.5))) 4. Concentric Gradient (Kind of weird for me but I liked the pattern) =MAKEARRAY(45, 45, LAMBDA(r, c, INT(SQRT((r-22)^2 + (c-22)^2)/5))) 5. Blocky Gradient (Pixelated) =MAKEARRAY(45, 45, LAMBDA(r,c, INT((r + c)/5))) 6. Top-Left Radial Gradient (Steep) =MAKEARRAY(45, 45, LAMBDA(r, c, (r + c)^2)) 7. Bottom-Right Radial Gradient =MAKEARRAY(45, 45, LAMBDA(r, c, SQRT((r-45)^2 + (c-45)^2))) 8. Diagonal Gradient (Sharp) =MAKEARRAY(45, 45, LAMBDA(r, c, ABS(r - c))) 9. Double-Diagonal Gradient (I like this one) =MAKEARRAY(45, 45, LAMBDA(r, c, r + c + ABS(r - c))) 10. Circular Gradient (Deep) =MAKEARRAY(45, 45, LAMBDA(r, c, INT(SQRT((r-22)^2 + (c-22)^2)))) 11. Wave Gradient (Vertical Ripples) It may look cool if you mix the green colours otherwise with white, it will turn out pretty bad. =MAKEARRAY(45, 45, LAMBDA(r, c, SIN(c/3)*10)) 12. Zigzag Horizontal Pattern =MAKEARRAY(45, 45, LAMBDA(r, c, MOD(ROUND(SIN(r/2)*10, 0), 20))) 13. Offset Circular Gradient =MAKEARRAY(45, 45, LAMBDA(r, c, SQRT((r-15)^2 + (c-30)^2)))
I am grateful for your compliments. Ha Ha, it's not like I had them sitting in my toolbox. I was having an idea of what I could do with the MAKEARRAY Function. I have been using many of them for Excel Challenges and Competitions. I didn't know the names of the patterns so I took the AI tool's help.
Very well done! MAKEARRAY is indeed the way to go, here. I made an 9-point star pattern as a background and kept the squares in the foreground. I also increased the resolution tenfold: looks better for gradients, IMO.
No cool formula I'm afraid but interesting to know that apart from being 45 squared, you can also get to 2025 by adding 1 cubed through 2,3,4,5,6,7,8 and 9 cubed. Someone else worked that out but i thought it was too cool not to share.
How about this formula in cell C1 : =A1-B1 A1 is a cell named: CostOfPayingAProperGraphicDesigner B1 is a cell named: CostOfAFewCompetitionPrizes C1 could then be given a cell comment: Money Bill saves by getting his social media followers to do the work Come on Bill, this is so cynical. A competition where the financial benefit to you hugely outweighs the paltry cost isn't a good look.
It's called unconditional love. We love Bill's challenges. His contribution to Excel and to the Excel community in general is second to none. And that is Priceless.
Great challenge!!
Math facts:
SUM(SEQUENCE(n)^3)=SUM(SEQUENCE(n))^2 for any "n"
for n=9 1+2+3+4+5+6+7+8+9=45 or SUM(SEQUENCE(9))=45 and 45^2=2025
Because of 9 , my idea went somehow to SUDOKU games, the coolest and most popular puzzle game related with first 9 nr.
This can be a challenge, Creating and/or Solving an array of 5x5 SUDOKUs.
It's a little bit more complicated than inventing random patterns, so if you like the idea let me know.
It will reflect the real power of what Excel can do these days with simple formulas/functions to solve such a popular game.
Excellent - I saw this elsewhere. 1 cubed + 2 cubed + ... 9 cubed is very impressive.
They also had (20+25)^2 = 2025
and a comment added had 1^0 + 2^0 + ... + 2025^0
Yes! And over time they become increasingly rare. In 4 AD you would have to wait a whole 5 years for that "rare event" to happen again!!
Best wishes for 2025 for you and Mrs.Excel.
I tried a bunch of things, and here is my final approach:
I applied a three-color scale to my grid using a dark green for both the lowest and highest values, and a lighter green for the 45% percentile. I used the Excel logo colors, hexacodes 185B37 for dark green and 3C381 for light green.
With that set up, what I wanted to do next is to use a formula to return zeros for all the numbers that have a square component. In other words, if either the row or the column is a square number it returns a zero, otherwise a one. That would be this formula: =ROUNDUP(MOD(SQRT(MAKEARRAY(45,45,LAMBDA(X,L,X*L))),1),0) but I didn't like the image it created, so I multiplied the array with itself before taking the mod. =ROUNDUP(MOD(SQRT(MAKEARRAY(45,45,LAMBDA(X,L,X*L)))*SQRT(MAKEARRAY(45,45,LAMBDA(X,L,X*L))),1),0) I am not sure what it is doing but it will work.
I gave that formula a defined name: "Buy_the_Book"
I then created this elegant formula: =MAKEARRAY(45,45,LAMBDA(X,L,POWER(X,L)))*Buy_the_Book
The result is a quasi-random pattern that looks like a maze. But it is not random; it is symmetrical! I liked it. It also looks like a QR code, which would be really neat.
You can also take out the Buy_the_Book portion and get a new arching visual that is kind of neat.
You could implement Conway’s Game of Life or Langton’s Ant on a 45x45 grid starting from some simple pattern (like a big XL), and see if it comes up with an interesting pattern… it wouldn’t be easy to do in one formula, although these days everything is possible!
There is also the mandelbrot
First comment. Happy new year sir. I would like to see a tutorial about how can you provide 6 random numbers that has a range form 1-42 in excel. Providing it, is much appreciated 🙏🤍
It's very bad luck to wish someone happy new year before the change. I hope Bill isn't struck by lightning whilst celebrating tonight.
Use the this formula =randbetween(1,42) in 6 different cells
@Geevs80 that could return six results the same....
@@ricos1497 doesn't for me, try hitting the F9 key
@@ricos1497 Ok I see what you are asking now. This this formula: =CHOOSEROWS(SORTBY(SEQUENCE(42),RANDARRAY(42)),SEQUENCE(6))
Here's my submission! I used a recursive Mandelbrot fractal algorithm and then zoomed in until I liked what I saw. Hope you like it!
Here's the formula (sorry it's not formatted, YT keeps deleting it so had to make do it Bo style!)
=LET(xleft,-1.98,xright,-1.4,ytop,-0.1,ybottom,0,size,45,iterations,10,fnMandelbrot,LAMBDA(xleft,xright,ytop,ybottom,size,iterations,MAKEARRAY(size,size,LAMBDA(c,r,LET(x_0,xleft+(r-1)*(xright-xleft)/size,y_0,ytop+(c-1)*(ybottom-ytop)/size,fn,LAMBDA(ixy,iteration,LET(i,INDEX(ixy,,1),x,INDEX(ixy,,2),y,INDEX(ixy,,3),repeat,AND((x*x+y*y)=iteration-1),newi,IF(repeat,iteration,IF(i
TH-cam won't let me post the formula for some reason, it keeps deleting my comment!
I emailed it to you instead, Bill. Does anyone know the trick to pasting large complex formulas in the comment section???
Here are some of my ways to have gradient. I am just going to use One Cell Formula with MAKEARRAY
1. Radial Gradient (Circular)
=MAKEARRAY(45, 45, LAMBDA(r,c, SQRT(r^2 + c^2)))
2. Center-Radial Gradient
=MAKEARRAY(45, 45, LAMBDA(r, c, SQRT((r-22)^2 + (c-22)^2)))
3. Wave Gradient (Sine Wave) You can actually play wit the 22.5 here and it will be pretty amazing
=MAKEARRAY(45, 45, LAMBDA(r,c, SIN(r/22.5) + COS(c/22.5)))
4. Concentric Gradient (Kind of weird for me but I liked the pattern)
=MAKEARRAY(45, 45, LAMBDA(r, c, INT(SQRT((r-22)^2 + (c-22)^2)/5)))
5. Blocky Gradient (Pixelated)
=MAKEARRAY(45, 45, LAMBDA(r,c, INT((r + c)/5)))
6. Top-Left Radial Gradient (Steep)
=MAKEARRAY(45, 45, LAMBDA(r, c, (r + c)^2))
7. Bottom-Right Radial Gradient
=MAKEARRAY(45, 45, LAMBDA(r, c, SQRT((r-45)^2 + (c-45)^2)))
8. Diagonal Gradient (Sharp)
=MAKEARRAY(45, 45, LAMBDA(r, c, ABS(r - c)))
9. Double-Diagonal Gradient (I like this one)
=MAKEARRAY(45, 45, LAMBDA(r, c, r + c + ABS(r - c)))
10. Circular Gradient (Deep)
=MAKEARRAY(45, 45, LAMBDA(r, c, INT(SQRT((r-22)^2 + (c-22)^2))))
11. Wave Gradient (Vertical Ripples) It may look cool if you mix the green colours otherwise with white, it will turn out pretty bad.
=MAKEARRAY(45, 45, LAMBDA(r, c, SIN(c/3)*10))
12. Zigzag Horizontal Pattern
=MAKEARRAY(45, 45, LAMBDA(r, c, MOD(ROUND(SIN(r/2)*10, 0), 20)))
13. Offset Circular Gradient
=MAKEARRAY(45, 45, LAMBDA(r, c, SQRT((r-15)^2 + (c-30)^2)))
Wow, that is impressive! Do you just have this sitting in your toolbox? The Concentric Gradient looks like a target.
I am grateful for your compliments.
Ha Ha, it's not like I had them sitting in my toolbox. I was having an idea of what I could do with the MAKEARRAY Function.
I have been using many of them for Excel Challenges and Competitions. I didn't know the names of the patterns so I took the AI tool's help.
@thegaminglearning I think you just won yourself a prize 😅
@@terrylavelle1139, I am looking forward how others approch the problem. I am looking forward to learning some new patterns.
Very well done! MAKEARRAY is indeed the way to go, here.
I made an 9-point star pattern as a background and kept the squares in the foreground. I also increased the resolution tenfold: looks better for gradients, IMO.
No cool formula I'm afraid but interesting to know that apart from being 45 squared, you can also get to 2025 by adding 1 cubed through 2,3,4,5,6,7,8 and 9 cubed. Someone else worked that out but i thought it was too cool not to share.
How about this formula in cell C1 : =A1-B1
A1 is a cell named: CostOfPayingAProperGraphicDesigner
B1 is a cell named: CostOfAFewCompetitionPrizes
C1 could then be given a cell comment: Money Bill saves by getting his social media followers to do the work
Come on Bill, this is so cynical. A competition where the financial benefit to you hugely outweighs the paltry cost isn't a good look.
It's called unconditional love. We love Bill's challenges.
His contribution to Excel and to the Excel community in general is second to none. And that is Priceless.