We made a bourgeois dirt cake by frosting it with chocolate frosting, covering it in cake crumbs from the discarded cake pieces! Cut out the center and slice off a tiny bit of the upper left corner. Then, connect the pound cake to the cut corner. This is the easiest number. We made a 6 stage alarm fire truck, so we covered it in red frosting, made a ladder out of pretzels, oreos for wheels, and a licorice hose!
Just kidding, THIS is the easiest one! Cut into three slices, cut the middle slice in half diagonally. Discard the right slice. Flip the left slice up horizontally and connect the other two slices beneath it. To decorate the ocean, we added in swedish fish and Teddy grahams with lifesaver gummy inner tubes. To decorate the beach, we cut fruit roll ups into squares and used them as sunbathing towels for the Teddy grahams.
Cut out the centers of the circle cakes, and then slice two edges. Connect the cakes.
Life Stage Numerology
We made an 8 race track, so we covered the cake in black frosting, piped some green grass, and used Good N Plenty candy to make the lines in the road. This one is the 6 cake flipped upside down. Because we at So Yummy acknowledge that Pluto is a planet ohanameansfamily , we decided to make a galaxy cake out of the number nine to honor all nine planets. We started with a base of black frosting, then swirled in blue and purple frosting and speckled it with white food coloring. Add some candy planets and star sprinkles for an out of this world cake!
Slice the pound cake in half. Cut the center out of the circle cake and then slice it in half. Separate the circle halves and fill in the gaps with the pound cake halves. We decided to make a pineapple cake by piping yellow frosting through a small star tip all over the cake. Then just pipe on a smiley face and some leaves to finish it up! Come here often? Subscribe to our newsletter. Yummy Recipes. By: So Yummy. Click here to load earlier stories.
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Gift Guides. Deirdre Durkan. Karen Belz. Read Just One More. This yields. Therefore, the expression above is not only an approximation, but also an upper bound of p n. The inequality.
Solving for n gives. Now, ln 2 is approximately Therefore, 23 people suffice. Mathis cited above. This derivation only shows that at most 23 people are needed to ensure a birthday match with even chance; it leaves open the possibility that n is 22 or less could also work. In other words, n d is the minimal integer n such that. The classical birthday problem thus corresponds to determining n The first 99 values of n d are given here:.
A number of bounds and formulas for n d have been published. In general, it follows from these bounds that n d always equals either. The formula. Conversely, if n p ; d denotes the number of random integers drawn from [1, d ] to obtain a probability p that at least two numbers are the same, then. This is exploited by birthday attacks on cryptographic hash functions and is the reason why a small number of collisions in a hash table are, for all practical purposes, inevitable.
The theory behind the birthday problem was used by Zoe Schnabel  under the name of capture-recapture statistics to estimate the size of fish population in lakes.
The basic problem considers all trials to be of one "type". The birthday problem has been generalized to consider an arbitrary number of types. Shared birthdays between two men or two women do not count. The probability of no shared birthdays here is. A related question is, as people enter a room one at a time, which one is most likely to be the first to have the same birthday as someone already in the room? The answer is 20—if there is a prize for first match, the best position in line is 20th. In the birthday problem, neither of the two people is chosen in advance.
By contrast, the probability q n that someone in a room of n other people has the same birthday as a particular person for example, you is given by. Another generalization is to ask for the probability of finding at least one pair in a group of n people with birthdays within k calendar days of each other, if there are d equally likely birthdays. Thus in a group of just seven random people, it is more likely than not that two of them will have a birthday within a week of each other.
The expected total number of times a selection will repeat a previous selection as n such integers are chosen equals . In an alternative formulation of the birthday problem, one asks the average number of people required to find a pair with the same birthday. If we consider the probability function Pr[ n people have at least one shared birthday], this average is determining the mean of the distribution, as opposed to the customary formulation, which asks for the median.
How Common is Your Birthday? This Visualization Might Surprise You
The problem is relevant to several hashing algorithms analyzed by Donald Knuth in his book The Art of Computer Programming. An analysis using indicator random variables can provide a simpler but approximate analysis of this problem. An informal demonstration of the problem can be made from the list of Prime Ministers of Australia , of which there have been 29 as of [update] , in which Paul Keating , the 24th prime minister, and Edmund Barton , the first prime minister, share the same birthday, 18 January. An analysis of the official squad lists suggested that 16 squads had pairs of players sharing birthdays, and of these 5 squads had two pairs: Argentina, France, Iran, South Korea and Switzerland each had two pairs, and Australia, Bosnia and Herzegovina, Brazil, Cameroon, Colombia, Honduras, Netherlands, Nigeria, Russia, Spain and USA each with one pair.
Voracek, Tran and Formann showed that the majority of people markedly overestimate the number of people that is necessary to achieve a given probability of people having the same birthday, and markedly underestimate the probability of people having the same birthday when a specific sample size is given. The reverse problem is to find, for a fixed probability p , the greatest n for which the probability p n is smaller than the given p , or the smallest n for which the probability p n is greater than the given p.
Some values falling outside the bounds have been colored to show that the approximation is not always exact.
How Common is Your Birthday? This Visualization Might Surprise You | The Daily Viz
A related problem is the partition problem , a variant of the knapsack problem from operations research. Some weights are put on a balance scale ; each weight is an integer number of grams randomly chosen between one gram and one million grams one tonne. The question is whether one can usually that is, with probability close to 1 transfer the weights between the left and right arms to balance the scale. In case the sum of all the weights is an odd number of grams, a discrepancy of one gram is allowed. If there are only two or three weights, the answer is very clearly no; although there are some combinations which work, the majority of randomly selected combinations of three weights do not.
If there are very many weights, the answer is clearly yes.
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The question is, how many are just sufficient? That is, what is the number of weights such that it is equally likely for it to be possible to balance them as it is to be impossible? Often, people's intuition is that the answer is above Most people's intuition is that it is in the thousands or tens of thousands, while others feel it should at least be in the hundreds.
The correct answer is The reason is that the correct comparison is to the number of partitions of the weights into left and right. Arthur C. Clarke 's novel A Fall of Moondust , published in , contains a section where the main characters, trapped underground for an indefinite amount of time, are celebrating a birthday and find themselves discussing the validity of the birthday problem. As stated by a physicist passenger: "If you have a group of more than twenty-four people, the odds are better than even that two of them have the same birthday.
The reasoning is based on important tools that all students of mathematics should have ready access to. The birthday problem used to be a splendid illustration of the advantages of pure thought over mechanical manipulation; the inequalities can be obtained in a minute or two, whereas the multiplications would take much longer, and be much more subject to error, whether the instrument is a pencil or an old-fashioned desk computer. What calculators do not yield is understanding, or mathematical facility, or a solid basis for more advanced, generalized theories. From Wikipedia, the free encyclopedia.
For yearly variation in mortality rates, see birthday effect. For the mathematical brain teaser that was asked in the Math Olympiad, see Cheryl's Birthday. Main article: Birthday attack. In particular, many children are born in the summer, especially the months of August and September for the northern hemisphere  , and in the U. In Sweden 9. See also: Murphy, Ron. Retrieved International Journal of Epidemiology.