Diarmuid Early

@KDCochran1 @ShengwuLi I remember that debate, and the theorem 😂 (One of many in which Shengwu claimed that 'everything the other side has said is irrelevant'!) Just when I thought I was done with posting on Twitter...

One reason I ‘retired’ from debating was the day that I had a winning argument that was -provably- true, but the proof was impossible to convey without 20 minutes and a whiteboard.

My solution to #ThisWeeksRiddler Express, in one Excel formula, explained in one minute. @xaqwg youtube.com/shorts/kiNelpk…

@xaqwg Riddler extension for this week: what's the biggest number that can't be encoded in a triple (m,n,q), as a function of q? With a modified Chicken McNugget Theorem and some Fibonacci magic, you can show it's F_q * F_(q+1).

@LaurentLessard @xaqwg Nice write-up, as always Laurent! On your question at the end, there are infinitely many solutions. One way to see that: any 8 primes in arithmetic progression work, and there exist arbitrarily long APs of primes (ref: en.m.wikipedia.org/wiki/Green–Tao…).

#ThisWeeksRiddler asks: is it possible to label vertices of a cube with distinct prime numbers so that the label sum for each face of the cube is the same? @xaqwg Yes, and in many ways! All solutions also satisfy nice symmetry properties. My write-up: laurentlessard.com/bookproofs/a-c…

@ptrajeev @xaqwg @LaurentLessard @HectorPefo I know the feeling : ) I thought it must have been about 2 years since I posted a solution - was a little jarred to find that it’s been almost 5!

@DimEarly @xaqwg @LaurentLessard @HectorPefo Hi @DimEarly - I do although I have had a dry patch of late. I do intend to get back into it. Just things with kids schedules :)

For #thisweeksriddler, it's easier to see the pattern if you look at the number of cells being added in each generation. @xaqwg @LaurentLessard (@ptrajeev, @HectorPefo - do you guys still do this?? Admittedly, I haven't been around here for a while...)

@ollie @wwnorton Finally got to buy this today. Congrats @ollie, looking forward to reading it!

@ollie @wwnorton

Using @FiveThirtyEight data and @msexcel to pick the best teams for my @premierleague pool - a short (OK, medium...) guide. youtu.be/3-rEY8RhN18

@MrExcel Here's one way (with "XFD" in A1): =LET(OneToN, SEQUENCE(LEN(A1)), Chars, MID(A1,OneToN,1), CharNums, DECIMAL(Chars,36)-9, SUM((CharNums)*26^(LEN(A1)-OneToN))) This works with longer strings too - e.g. if we ever get there, this says col ABCDE will be #494,265

In Excel, column XFD is the 16384th column2^14). Is there any elegant way using BASE or DECIMAL to convert XFD to 16384? My was is slow and clunky. quora.com/Can-we-calcula…

@ollie Someone needs to set AlphaZero loose on this thing. I want charts.

@xaqwg I took a stroll down memory lane for the classic - this lemma from my PhD thesis came in handy!

@chapmajw @xaqwg Oops, you're right, I was looking at the one next to it. So your 9 is right. To be honest, I did it mostly by hand, with some help from Excel. I should have been more careful!

@chapmajw @xaqwg Snap! Except I have one different from you - I think your 9 in the 7th row and 7th col should be a 6 (you can move 2 up from there to get to the 5). Full disclosure - I used yours to fix a mistake in my first version too!

@lotterdata @xaqwg I think you can take it a (small) step further - there's always a max unless D and P share a common factor, and in that case you use a similar formula to get the max mult of their GCD.

@xaqwg The maze should have been the classic - so much to it! Some extensions: Can you finish from every starting square? Which start is most moves away from the finish? (Interestingly, there's a unique answer, and it's adjacent to the finish square!)

@lotterdata @AtDrunkTweeting @xaqwg @Mathgarden You’re right, of course - thanks. Will have to trim my planned stadium a little...

@lotterdata @AtDrunkTweeting @xaqwg @Mathgarden Do you see more than one way to get two consecutive with -1 or -2? It has to be the highest power of 2 and an adjacent prime, and as long as you’re below n = 2^82,589,934 that’s n/2 and n/2 - 1 (I think).

@AtDrunkTweeting @xaqwg @Mathgarden A couple more extensions to push this further... if the stadium size has to be between 2 and 100,000, which possible sizes work? If the stadium size is unlimited, what's the largest known size the claim could work for? I think it's 2^82,589,934 - 1.

@xaqwg @Mathgarden As an “extension” am I correct that this problem works with 10, 20, 40, 200, and 300 seats but NOT 100?

@HectorPefo @xaqwg I read it as meaning you can pick a pace for any probability p (so you’re really just picking p) - seems reasonable to assume there is some pace at which a competitive team can almost surely finish the distance.

@xaqwg I'm years ahead of this one! (From back in the day when I found time to write about my solutions...) theexcelements.com/2016/07/07/ten…