Maths and Science discussion forum

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Make 24 puzzle of the day:

Create 24 using 2, 3, 5, 12, using each of them once and only using the 4 elementary operations

First to solve gets 5 club points

This is actually the hardest make 24 question, according to a website I use

Thats why it is puzzle of the day, DAY, it is meant to be challenging and it might take people 1 whole day.

33

easy, 3x/9=11, so x/3=11, so x=33

you are free to ask questions you don't know

How to prove the recurrence relation for Catalan numbers? I need help with this.

what is log4?

um it is irrational, are you asking for an approximation? if you want an approximation search on calculator.

Question of the day: Prove that log(4) is irrational

Note that it is base 10 log

Answer to last time's question: 24=12/(3-5/2)

Answer to day 2 question:

Let us use contradiction. Assume log(4)=p/q. Then, 10^(p/q)=4. But, raising both sides to the qth power, we get 10^p=4^q. But, 10^p is a multiple of 5 while 4^q is not. So, log(4) is not p/q, therefore log(4) is irrational.

Day 3 question (From Blitzstein-Hwang Probability edition 2 Unit 4):

Find values of w,b,r such that the Negative Hypergeometric distribution with parameters w,b,r reduces to a Discrete Uniform on {0,1,2,...,n}.

Nobody? Remember every solve gains you 5 club points!

Day 3 answer: 1, n, 1

ok, new daily question

could you post the day 4 question thanks

Day 4 question:

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000.