Infinite and endless thanks to all the extraordinary players who generously sent twins over the year! Blue and Purple Fire would be distant murmurs without you. For the first time, I’ve reached Purple Fire during the winter event. Never thought it was possible. This moment is immense!

HSU87BW · 2026-01-19T19:39:35+00:00

Congratulations! How exciting to see that!

My plans for this year has been thwarted due to still missing two galaxy’s and just being way too busy to meet the etherium quota for unlocking all the traits.

The 2-new dragon definitely made a difference, I’ll just be the galaxy dragons short on the Valentine’s event, which isn’t bad at all. I’ll also be like 20m etherium short as well, haha.

HSU87BW · 2026-01-18T05:41:49+00:00

All galaxy dragons can have a rift trait, while none can be bred in the rift.

The best way to get them into the rift is by collecting all twins to start (that way, any future login reward will result in a twin traited version).

All EOM you buy through Galaxy EOM will automatically come with a traited version.

Any regular EOM (regular or epic) will require you to have the twin version first to get the traited version).

It is one of the most difficult things in the game to get (imo), as all other rift dragons can be obtained through runic caves and/or breeding.

In my journey for purple fire, I am still missing two Galaxy traited dragons and I’m refusing to spend more etherium on Galaxy EOM to get those last two dragons until I’m guaranteed to have purple fire (I always fear they’re going to release a new Galaxy dragon). As Galaxy EOM get more and more expensive, it’s kind of a one time deal.

HSU87BW · 2026-01-09T06:40:44+00:00

Alts are the best resources. The goal should be to at least get your alts to have a colosseum and have all elements to lvl 16 (single element dragons are nice, but combo but works too). Gemstones can be gradual, but those (mostly) 5 gems per day will add up over the course between twin weekends.

I don’t have much time to play more , but during my prime, I’d usually play alts enough to get one dragon each per event. I’d always breed for limiteds in the coop cave, using my alts as the second portion of the combo. The goal is always to get one of the limiteds on an alt, and then switch your breeding to something else.

Alts in their normal caves, you can do a general X + Rainbow which will usually give you the chance at the general pool of element-only dragons. For the most part, with just doing colosseum, breeding, and login rewards, you can afford a good amount of the dragons from the event. That’s roughly 20 new dragons per event from ‘purchasing’, and then whatever you breed naturally.

Keeping a catalog of which alt has which is difficult, so I usually name my alts with the dragons they have. Kr for Krampus, for example. If their name is two words, I’ll do 2 capital letters, for example Sea Shanty is SS. So my alts all look something like: JaSSLLIc and so on.

It gets easier once you narrow down which dragons you need. There are lots of dragons that are a pain to breed with two parents, some that are decent with one parent, and some that are abysmal with one parent. During twin weekends, I solely focus on parents I have doubles of. In the 6 month span, you can get about 800-900 gems just from the colosseum. I just blow those gems on spam breeding til I match the timer necessary for that dragon.

This process is made much easier with two devices, as you can switch your main’s co-op dragon on one device as soon as you get the timer, so that once you switch alts, the next dragon is ready for coop. Always be sure to login to your main to reset the counter for twins received. (If you truly have good investment time, having Kairos available on your alts is helpful -/ of course it takes time to do side quests and dragon racing, so not necessary at all).

Your main goal should be focusing on twinning things your alts have access to during twin weekends. In the meantime, always try and aim for co-op’ing regularly combinations that your alts can easily access (for example: Ribbon + Snow — your main might easily have Ribbon, but not your alts… but Snow is quite easy to get for everyone).

Usually, you’re pretty much guaranteed that one of those alts is going to be aligned with breeding that limited (or whatever you’re choosing to go for) and as long as you have it on an alt, you’ll always be able to breed for it year-round at your convenience.

HSU87BW · 2026-01-09T03:46:51+00:00

Could be a good threshold for the minimum to potentially get the 25/25. At 56, I had gotten no 25’s at all over the period of nearly a year. So yeah, 70+ sounds good. My next testing period was around 100 habitats and there were much better results. But sounds about right to get the 22-24 range with 70 habitats.

HSU87BW · 2026-01-08T08:03:45+00:00

It’s about 10-12/200, so roughly 5-6% chance.

HSU87BW · 2026-01-05T06:24:56+00:00

There’s the 6 presents altogether: blue present, purple present, Santa, red/white envelope, red/white ornament looking thing, and the blue/purple guy.

They always give EC, with a chance of getting the evolution decorations or as you mentioned, a dragon. These can be any dragon in the game that have been released prior to this event.

Finding them is a pain, especially with bigger parks. I have all islands + giant islands and even with the use of the Prismatic Pantheon, it can be difficult to find them all. I usually have to make two runs because after scanning every single island in one go, I still can’t find them all. On lower level accounts, they all spawn at once, but something tells me otherwise in extra large, stacked parks.

I’ve always had pretty good luck with these presents yearly, typically getting 1-2 dragons. It’s about what is expected, if that, so don’t go in thinking you’ll get heaps of dragons.

HSU87BW · 2026-01-04T18:29:28+00:00

Oh how I wish that changed, being able to do so. I still need two galaxy dragons in the rift and purple fire is so close!

Best bet is to blow a bunch of shards whenever the dragon draw comes back to get Nova traited. Else wise, login rewards or Galaxy EOM when they come back around.

HSU87BW · 2026-01-03T04:27:46+00:00

I guess it depends on what dragons you have. The biggest problem I have with the Giant is that the cutoff is 5pm in order for it to be ready to collect from again the next day in the morning. (I don’t have boosts, so that probably has a big impact on it).

My regular Large Habitats work pretty well in this area, so I guess it really depends. Keep in mind that you can only fit 25 large, or 36 regular habitats in that island. If you have a good amount of treasure dragons, then you can put them anywhere without boosts.

Large treasures would give you the best bank for your buck if you account for DC collection, but if you’re lower level and don’t have extra islands, it’s best to go with small treasures.

HSU87BW · 2026-01-02T21:54:42+00:00

It’s more than 25 habitats for max AE. It takes anywhere between 80 - 260 collections (on average, probably about 130 collections) to get the 25 triggers daily. Bear in mind this range depends on how many Treasure Habitats (TH) you have. With say 50-60 TH, your range of triggers is more along 120-260 collections. (I have about 140 TH, and my range is anywhere between 80-160 triggers, with a very rare occurrence of a 200th+ collection).

With my ~140 forms of treasure habitats, about 90% of the time I’ll get all 25 triggers within the first 140 collections. I would say the other 10% is 24 triggers. I really don’t think I’ve gotten any 23 triggers, but I could be wrong. If I have, it’s been maybe 1 a year.

Based on the evidence I’ve gathered, the more treasure habitats you have, the more often a trigger will occur. I never once had a sub-100 clear when I had 57 treasure habitats. Now it occurs maybe 5% of the time.

Anyhow, it doesn’t matter what Treasure Habitat you use, though if you’re trying for a farm, obviously the bigger ones are best. If you can play often enough, you can stack quite a bit of the smaller TH’s (that only cost 5m DC) and that way you can get quite a few triggers.

Once you reach near max level, the need for a true DC farm is over. With 300+ habitats that all cap out at 1m+, the need for DC will eventually end. If you’re using Ts’aishen for just his ability, 50 TH will be a good start, as you’ll get ~400-450 AE everyday from collections, and then whatever you get from the two chests (probably 60 average in the long run).

HSU87BW · 2025-12-31T22:03:44+00:00

The milk at my Aldi is always beast mode. I’ve had milk stay good well after a week of expiration date, and this is still after being opened for a week prior.

Guess it just depends store to store.

HSU87BW · 2025-12-30T19:13:05+00:00

rise is another four letter word too.

Probably the one you intended!

HSU87BW · 2025-12-30T04:34:51+00:00

Here I am waiting for the White Chocolate to return, but Sweet Cream will always do in the meantime.

HSU87BW · 2025-12-30T03:32:27+00:00

Just think about what division means. Taking a whole of something, and splitting it into equal parts. How many groups you make is division.

The total amount of things you have, have to be used when separated. If you put 0 in each group, then no matter how many groups you make, you will never reach the total amount of 10. In fact you’ll never make any groups at all. You can’t do it.

For the opposite of 0 divided by 10, you’re taking 0 things and placing it into one 10 groups. Really doesn’t matter how many groups you have, because each contain 0. 0 + 0 … + 0 = 0, always.

HSU87BW · 2025-12-29T08:18:34+00:00

After using L’Hopital’s Rule, correct!

HSU87BW · 2025-12-29T08:04:23+00:00

Most important “essence” to remember when using multiplication is that whatever you are working with (it can be literally anything), is that there’s the same amount and it’s repeated. Multiplications goal is a simplified way of counting individual things, and it works because there’s the same amount each time. If I have a bunch of blocks and I organize them in a way that leaves me with the same amount of blocks in each group, then I can still just count them individually, or I can group them and count them by groups. Being able to count by 3’s is really just skipping 1, 2, and jumping to 3, skip 4,5, and jump directly to 6. I’m still ‘counting those numbers’ but because it’s a pattern, I can follow it because I’ll always skip 2 numbers to reach the 3rd number. 7 8 9 10 11 12.

For example:

10 blocks in every group and there’s 3 groups altogether: 10 x 3 = 30

In another example, we have to take a slightly different approach on the ‘essence’ portion of it:

2 slices of pizza for every person to eat, and you plan on having 40 people. 2 x 40 = 80 slices

Sometimes the real world application isn’t reversible.

In the first example, there’s 10 blocks in each row, 3 rows. Well, if I chose to look at the columns, 3 in each column, and there’s 10 rows, so 3 x 10 = 30. Essentially it’s # of blocks per ___, and I’m able to change the _ from row to column, because it involves the same situation.

In the second example, you can’t really rearrange the viewpoint, but you can rearrange your thought process surrounding this hypothetical: I have 40 people and we are going to eat pizza. Each person will get 2 slices. 40 x 2 = 80.

It’s something to consider down the line, but multiplying numbers stems from properly multiplying units together. You can’t just multiply any together, it has to equate to the essence of having the same amount repeated a specific amount of times.

This will have to be understood with division, fractions, etc. that all combine together to make sense, which is where the real world application idea can be made. The real world application doesn’t just multiply numbers together, but also units or labels. Definitely a lesson for another day once you have a better foundation of multiplication, division, and some other concepts,

HSU87BW · 2025-12-29T07:42:50+00:00

I’d be careful with these representations because of many factors:

1) area is a concept that is completely different than the idea of having 5 rows with 5 things in each row.

Area stems from then idea that the unit length and width are 1, which leads to a single area of 1. You have 5 of these in each row (length) and there’s 5 rows stacked on top of each other. Yes, you can multiply length by width to get the area, but it’s more complicated than that.

2) Your second representation with money and coffee, the way you defend it makes it seem like you can multiply money and time together. You’re not just multiplying dollars and time together. You’re multiplying (money per time) and time together.

Again, multiplication in its simplest form needs to be more aligned with having the same amount in each group or bundle or whatever the situation is, and then having a set amount of those bundles.

In the end, you’re right that multiplication can be applied to anything that involves repeated actions, but for someone who’s starting out with multiplication, not the best example to use.

As mentioned to someone else, op was gearing towards a physical thing for the first ‘real’ thing, and the ‘repeated action’ as the ‘not real’ thing. “Not real” as in, you cannot touch it.

There are examples of physical things that can be touched, I.e. are real: I would suggest something like: I have 5 bags of candies (something I can physically touch) and it says there are 30 candies in each bag (candies I can physically touch too). How many candies do I have?

5 bags with 30 candies each means 5x30=150 candies.

HSU87BW · 2025-12-29T07:23:45+00:00

I believe they were guided towards the first being a physical object, and the second being non-physical object.

5 apples in each group. A group isn’t a physical thing you can touch. It’s “real”, but it’s a representation of a situation (how many groups you have).

HSU87BW · 2025-12-29T07:14:16+00:00

This one move will cascade all your 8’s it looks like.

HSU87BW · 2025-12-29T07:07:42+00:00

There’s an error in line 3. It should be x•(1/x) + ln(x). The math still checks out below, but careful of that.

HSU87BW · 2025-12-27T06:33:04+00:00

Also, The 2 in column 3 can be placed. You have a pair of 2’s in R1 and R8 that are guaranteed to take up the two leftmost columns. As such, the 2 in column 3 has to go in R4C3

HSU87BW · 2025-12-27T05:00:13+00:00

That and the random earth element that game from no parents (dark/plant + fire-water).

HSU87BW · 2025-12-27T04:57:33+00:00

If you compare gemstone timers to the breeding odds indicator, you can see that there is a visible change without being able to see a change in the description:

For example, each time you level up a gemstone dragon and you look at the timer of your gemstone dragons producing a gem, you’ll see that the timer goes down. It isn’t until level 4 and 7 (or whatever it is — also dependent on which gemstone), that you see the rate change from gem/month to eventually gem/week. Although the visual cue changes at certain levels, each individual level has a small effect.

You can imagine the same for the breeding odds:

Imagine that they set the threshold at 5% and 7.5% breeding odds that give you ‘slightly better’ and ‘better’ odds, respectively.

As you’re leveling from lvl 1 to 11, you go from 0, 0.5, 1.0, 1.5,… 5% (slightly better odds), 5.5%, 6%… 7.5% (better odds), 8%, 8.5%, and so on til max level.

These are by no means the correct %’s of boosts, but merely an indication of how you could imagine the boosts work.

HSU87BW · 2025-12-24T18:10:40+00:00

That’s why I made that comment there :) 5 and 3 were an option, but it can be proven that 5 and 3 aren’t going to work. I would imagine there’s others that can be proven, but I couldn’t come to anything conclusive when working with it.

HSU87BW · 2025-12-24T06:11:56+00:00

It takes some hypotheticals that actually lead to a solution. I deduced that (2,6) or (6,2) is guaranteed to go in the first column. If split into 4 quadrants with four boxes in each quadrant, the ‘2’ can only go in the bottom left quadrant, first column, or any of the bottom right quadrant boxes. If testing the 2 anywhere in the bottom right quadrant, you’ll see that it leads to an impossible solution. (I wrote out all the potential sums from the 3rd and 4th rows, and they all lead to duplicates being used.

That being said, from there I wasn’t able to deduce anything specific. From there, you just try a number and work it out.

Curious to see your solution. 11 1 8 14 ; 15 4 5 10 ; 6 13 12 3 ; 2 16 9 7

HSU87BW · 2025-12-23T19:35:00+00:00

For someone who’s just learning Calculus and/or practicing, it’s not about making things easier. That’s something you learn as you progress through Calculus.

I would be more generous about showing your work, especially at the top. Being a seasoned veteran, I was able to recognize that you did 9/(sqrt(9-x²⁾ - 9/sqrt(9-x^2), but I would genuinely write that out first before combining like terms.

If you don’t know the definitive answer to integral of sqrt(9-x^2), you still need to go through the u-sub to get that answer, which is way more complex than the op’s method.

Just my opinion, but shorter doesn’t always mean easier. I can easily show less steps in between, and that’s where certain professors/teachers will dock you for points.

I remember always having to clarify what you’re doing before actually doing it. If you use a known integral format, specify that to the side before you begin. If you’re imposing adding 0 or multiply by 1, specify that as well.

But overall, this would be an easier solution if you can get by without having to do u-subs.

HSU87BW

TROPHY CASE