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George Armstrong A bit more creative this week. For your bonus points, solve a target bang on after having repeated large numbers in the selection. This'll mean picking anything from 2L to 4L. The more larges you pick, the more likely the larges will repeat, but the less likely the target will be hittable. Good luck with your tactics here ;)

Adam Dexter Just a question, and for the avoidance of doubt: Is it a requirement that we attempt the bonus option? If I would prefer to hedge my bets at more solves by doing 1L, would this be outside the rules?

George Armstrong Not a requirement at all, and I predict a few more will opt not to in later rounds... ;)

Eoin Jackson Ok... this is starting to annoy me now. There are some smart people here, right? Some, dare I say, mathematically minded people?!

What are the odds of drawing duplicates if you select 2L? I've worked it out at 25%, but then I hate probability and am never confident with my calculations.

And then we have the more interesting one... what are the odds of drawing duplicates if you select 3L... This one I really can't figure out. I tried to do it using permutations and got 62.5%... but that's not right. Then I did it using combinations instead and got 75%... which is currently my best guess, but I may be forgetting about something important.

Can someone good with number pls help solve the mystery?

Tom Cappleman Easiest way is to work out the chance of no repeats. With 2L, the first one is arbitrary, and the second has 75% chance of being different. So 25% chance of a repeat.

With 3L, the second still has a 75% chance of being different from the first, and the second has a 50% chance of being different from both of them. So the chance of all 3 being different is 75%*50%=37.5%, giving a 62.5% chance of at least one repeat. So you were right first time

Tom Cappleman Which means that Florence's 3 rounds with repeats when picking 3L is astonishingly unlikely

Eoin Jackson Yes, such bad luck in Florence's game!

Thanks for that. Nice clear logic.
I would not have been confident with any guess of mine, and had definitely started to overcomplicate it.

Eoin Jackson Wait, I'm starting to get a taste for this now...

So the probability of duplicates with 4L has got to be 93.75%, right?! 😁

Tom Cappleman 90.625% I think. Chance of no repeats being 37.5% (from 3L) * 25%=9.375%

Eoin Jackson 😥 I'm guessing now is not the right time to admit to being a teacher of (the Irish equivalent of) A-level Maths?

Wesley Barton Do you get a bonus only if you get the target exactly, or can it be the closest possible?

George Armstrong Exact only - intention was to counter the higher probability 4L pick with lower probability solve rate ;)

Dan Spinks total stitch up, only 2 bonuses available. I was going to put in an official complaint when I'd only had 1 after 19 rounds

George Armstrong Wow and we thought Florence had it bad... :(

Wesley Barton Only 2L this time though, so 1/4 of the numbers being the same in any given round.

George Armstrong Fair point :)

Wesley Barton 7.6% of that many non-duplicates in Dan's game

Wesley Barton Not sure if I did the maths right

Wesley Barton I think it's actually 1.3%

Eoin Jackson Florence had it much worse, given the difference in picking strategies and the probabilities involved.

What I am interested to see is whether 2L is a smarter pick than 3L in the long run here... coz Dan's game score + bonuses is very competitive... so -unless you are in the absolute top 5% of Apto numberists- perhaps 2L is the way to go?

Adam Dexter Do I not get a bonus for R7? I was one away but that was the best available

Dan Spinks the reason I dodged 4l here was that if you do get a repeated number you then don't have the normal 4 large so you lose some of the normal 4L tricks which makes it harder to hit the target. I don't know if that's good logic though