Birthday problems
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Here is an idea: (Collaboration with Bob the Cat)
Bob the
opened a bakery with 6 type of birthday 
‘s and 18 type of desserts. On Po-Shen Loh‘s birthday, he selected a completely random sample of 24 (6+18) people, giving each person a random cake and a random dessert. What is the probability that the 24 people all have their birthday on June 18th and all received the same type of cake and dessert?
PS An early happy birthday 🥳 to Po-Shen Loh! -
@RZ923 Wow I didn't imagine you could combine the golden ratio, positions and probabilities all into one! Go Bob the Cat
! 
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Whoa what? Also umm how does golden ratio fit in lol
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@The-Darkin-Blade You're right, it's not exactly the golden ratio... maybe we should make it a rectangular cake with length 16 inches and width 10 inches
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We should add an extra part: We made a cake that is 62.28 inches in diameter because Prof. Loh deserves a special cake. How much space (volume) will the cake take up?
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Another problem:
Bob the baker is back!
He baked 28 small cakes that could bear the symbols: P,O,-,S,H,E,N,L,O,H,6,/,1 or 8. He generate a random symbol from the above list for each cake and put the symbols on them. (Yes, the letter O and H have the highest probability of 1/7 each, while the others 1/14 each)
But he accidentally messed up the cakes and have to randomly re-order them.
Then he uses Baker Cat Magic and have a 16.18% chance of switching the symbol on the cake currently to the next (ie P to O, S to H etc). O and H have 8.09% chance of going to - and 6 with the same chance for going to H and E, respectively.
Or else the symbol stays the same. The same applies for all symbols.
What is the chance that, in the end, it spells “PO-SHENLOH6/18PO-SHENLOH6/18” ? -
@RZ923 We're going to have a lot of fun with these, lol
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My brain power isnt enough to solve problems but I can surely make them
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@The-Darkin-Blade Me too
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Bob the
’s bakery was a success!
He cooperated with three big
companies - Po, Shen and Loh - to celebrate Professor Loh’s birthday.
On June 18th, the three companies makes random # of cakes between 24 and 618. Every possible # of cakes have equal chance. Then they press letters on each one.
Po company: 61.8% chance press P, 38.2% chance press O.
Shen company: 6.2% chance press S, 93.8% chance press H, E or N.
Loh company: 81.6% chance of press L, 18.4% chance press O or H.
Then they choose the best cake on display. Each cake have the same chance of being on display. Bob the take photos of the three displays and shuffles them into random order.
What is the probability that the photos spell Professor Loh’s initials (PSL) in the same order? -
Oh wow these are hard! Happy early birthday Prof. Loh! Mine is two days after yours
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@divinedolphin An early happy birthday to you too!!!
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An early happy birthday!
(To @po and @divinedolphin) -
It is Prof Loh’s birthday today!
Hooray!
4:19 PM in Victoria, 2:19 AM in Pittsborough. 18th June, 2020. -
Happy Birthday Prof. Loh!!!!
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HAPPY BIRTHDAY PROF. LOH!!!!
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Happy Birthday Po Shen Loh you now are going to do calculus and bunch of things like
: Po Shen Loh you did a really good thing for like calculus and integrals!! -
The Montgomery Blair Math Tournament or MBMT is a really good thing and Po Shen Loh the coach of the USA team for IMO will explain the problems!!
