Math Blob Run !FULL! Download

A Math Blob Run game is a game in a maze where you need to solve math problems. Join our courageous Math Blob as it races against a relentless Bad Blob, with only one way to escape - solving mental math questions at lightning speed.

With over 1000 math questions of all kinds, Math Blob Run is the perfect tool for anyone looking to practice their fast calculations in a fun and engaging way. The game features simple and intuitive gameplay, retro sound effects that will bring back nostalgic memories, and vibrant, colorful graphics that will keep you hooked for hours.

Math Blob Run Download

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Drag a blob to make it sing. Other blobs to the right of that blob will follow along. Each of the four blobs sings in a different vocal range: bass, tenor, mezzo-soprano, and soprano. Dragging up and down adjusts their pitch, and dragging left and right changes what vowel-sound they sing.

Click on a blob and drag it to make it sing. Other blobs to the right of that blob will follow along. Each of the four blobs sings in a different vocal range: bass, tenor, mezzo-soprano, and soprano. Dragging up and down adjusts their pitch, and dragging left and right changes what vowel-sound they sing.

All occupied cells in the grid are part of a single "blob": a single shape defined by a set of occupied coordinates for which each occupied coordinate has at least one occupied coordinate to either its top, left, bottom, and/or right.

A: Because we already know that the unbiased method works exactly the same way except you only accept the outcome of the random selection when the rules for a blob are applied "strictly" (i.e. you only have a blob when there's a single connected group of occupied spaces), and so if you instead just pick an occupied space and use its connected occupied spaces as the blob, you'll at the very least be biased towards smaller blobs.

A: Well, $\frac{|B|}{100}$ is just the probability that you choose one of the cells of the blob, assuming it exists. So presumably the other part is the probability that it was created. To make it easier to understand, note that in the first formula you see that the odds of getting the strict blob you want (strict because you're not tolerating occupied cells not part of your blob) on any particular attempt is $2^{-100}$, because you need all 100 of those coin-flips to go exactly the way you want them. So in this less-strict situation, you need the coin-flips for your desired occupied spaces to go the way you want, and you also need the coin-flips for the unoccupied neighboring spaces to go the way you want, so that there's no chance you'll have a neighbor end up occupied and change the blob to a different one.

A: Using a numerator greater than the probability of getting the rarest blobs (which is roughly $p^*$) will result in a non-uniform distribution, and using a numerator that's smaller will make the program take longer to run. The reason using a numerator greater than $p^*$ will result in a non-uniform distribution is that it will lead us to accept some not-rarest blobs with the same probability as the rarest blobs. If we have the numerator as $p^*$, then when we actually come across one of those rarest blobs, the $p(B)$ will equal $p^*$, and so the acceptance probability will be "1" (we'll always accept that blob). But if the numerator is larger, not only will we always accept the rarest blobs, but we will also always accept the less-rare blobs whose $p(B)$ is such that dividing the larger numerator by $p(B)$ will result in an acceptance probability of at least 1.

Step 1 is equally likely to generate each blob (as well as all the non-blobs), so the result (once a blob finally is generated) is equally likely to be any blob. More precisely, let $f$ be the probability that we get something that isn't a blob. Then the probability of generating your favorite blob $B$ on the $k^{\text{th}}$ trial is $f^{k-1} \cdot \frac{1}{2^{100}}$: we failed to get a blob $k-1$ times, and then finally got all the cells in $B$ and no others. So the overall probability of getting blob $B$ with this method is $\frac{2^{-100}}{1-f}$, which doesn't depend on $B$, and therefore all blobs are equally likely.

We choose a probability of $\frac12$ so that on each trial, any blob $B$ has the same probability of $2^{-100}$ of being generated. If the probability were $p \ne \frac12$, then the probability of generating a $k$-celled blob would be $p^k (1-p)^{100-k}$, which is not uniform.

Even though this method is definitely biased, it has the nice feature that we know exactly the probability with which a blob $B$ is returned in a single trial. That probability is$$ p(B) = \frac{|B|}{100}\left(\frac12\right)^{|B|+|\partial B|}$$where $|B|$ is the number of occupied cells in $B$ and $|\partial B|$ is the number of unoccupied cells bordering $B$. Moreover, we can put a lower bound on $p(B)$ for any $B$: it is $p^* = \frac{33}{100} (\frac12)^{100}$. (This is the minimum of $\frac{x}{100} (\frac12)^{x+y}$ over all $x,y$ with $x\ge2$, $y \ge 0$, $x+y \le 100$, and $y \le 2x+2$: the constraints on $|B|$ and $|\partial B|$.)

Now, on any given trial, the probability that $B$ is the blob we get after step 2 is is $p(B)$. But the probability that we actually return $B$ is that probability times the acceptance probability: $p(B) \cdot p^*/p(B)$, or $p^*$. So on any given trial, every blob has the same chance $p^*$ of being produced.

Unfortunately, this will bias things towards blobs of a size proportional to the percentage with which you make the cells black or white. For example, if you turn a square black or white with a chance of $50$%, then of course, you'd get almost all blobs with a size of around $50$.

EDIT: Not true. By setting the percentage of turning a cell to black or white to $50$%, the likelihood of each specific blob being the outcome of this process is the same as for any other specific blob.

So, you really want to avoid that bias ... and note that the method described in the post has a very similar bias, in how the size of the resulting blobs very much depends on the percentage your algorithm uses.

So, what to do? Can we calculate how many blobs there are of a certain size? Well, the number of possible blobs is of course really big. And I don't even see a simple formula for calculating an exact number or, for that matter, how many there are of a certain size. So I don't think it will be practical either to exactly pre-calculate these kinds of numbers so that you could randomly pick blobs of a certain size (let alone shape) proportional to how many there are of that size (or shape)

For a blob of size $n$: Randomly turn $n$ of the $100$ squares black or white, and see if you get a blob. Do this a large (but still practical) number of times, say $10000$, or maybe even $100000$ and just count how many times you get a blob. Do this for all $n$, and that should get you a rough idea for the proportions of blobs of a certain size, e.g if for $n=3$ you obtained a blob $20$ times out of $10000$, but for $n=40$ you got a blob $200$ times out of $10000$, then there should roughly be $10$ times as many blobs of size $40$ then blobs of size $3$, and that is because each specific blob (of whatever size, shape, or orientation) will be chosen with the exact same likelihood as any other blob.

(By the way, for some $n$ you will hardly get any blobs at all, e.g. I would not be surprised if you get $0$ blobs out of $100000$, or even $1000000$, for $n=20$ ... but that's ok: that just means that the number of blobs of size $20$, out of the whole space of possible blobs, is really, really small ... and so statistically you may as well set its proportion to $0$ relatively to other sizes. Also, for large $n$, say $n>80$, the chances of getting a blob become really good, so you can probably get away with just generating $100$ random square assignments. )

Once you have those proportions, then generate a random blob by first picking an $n$ relative to those proportions, and then randomly picking $n$ squares out of the $100$, and just keep repeating that until you get a blob.

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Hello, I am a lethargian and I am VERY I tell you VERY bad at math and I really need some help but all I really like to do is SLEEP sleeping is so fuuuuuuun! My who scedual is sleep then take a nap then sleep the wake up and then go for a 15 minute Nap it is very fun to sleep and it is fun to Nap I can't choose wich one is better Sleeping or Naping they are quite differnt and I try to swich off so they don't get mad at me when I Sleep to much or Nap to much, sooooooooooooooooooooooo.........you should get back with me but by the time that you try to get back with me I will probley be sleeping.

Commonly known as the California blackworm, the tiny invertebrate Lumbriculus variegatus has graciously shared a few of its secrets in a new study examining the math behind its incredible living knots.

In the new study, researchers from Georgia Tech and the Massachusetts Institute of Technology used ultrasound to shed new light on worm blobs, revealing details that could inform the design of robots with similar skills.

Blobbing helps them survive harsh conditions, like extreme temperatures or lack of water, that would kill lone worms. A worm blob can behave as a solid or fluid, research has found, and can even demonstrate collective decision-making. ff782bc1db