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Melody

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यूजर का नामMelody
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Melody  11 Feb 2022
 #62
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Excellent work Walt and Reinout-g,

I want to take a look at these answers and think about how they may have been done.

First I will look at Reinout-g's
the numbers were
3,8,9,10,10,50 with magic number 276

I can think of 2 different ways that Reinout may have reached this answer.

(1) 3,8,9,10,10,50 with magic number 276
276
= 300 - 24
=3 x 100 - 3 x 8
okay, we only have 1 three so you think that isn't helpful.
Well you are wrong because I am going to factorise out the 3!
You don't need letters to be able to factorise
= 3(100-8)
= 3 x (10 x 10 - 8)
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(2) 3,8,9,10,10,50 with magic number 276
276
I know that 3 goes into 276 because 2+7+6=15 and 3 goes into 15 therefore 3 goes into 276.
(Anyone who has followed the "what a number is divisible by will know this!) therefore
=3 x 92
=3 x (100-8)
=3 x (10 x 10 - 8)

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Then Reiner left a new one which Walt solved.
3,11,22,33,44,55 with magic number 333
I also got a different solution to WALT so I will show you both. (I am going to do mine first because I thought it was easier.)
But, walt's brain obviously works differently from mine so probably doesn't agree

3,11,22,33,44,55 with magic number 333
(1) 333
= 330 + 3
= 33 x 11 + 3
or
(2) = 33 x (55-44) +3
or
(3) = 33 x (22-11) +3
There are probably other answers along this line as well.
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Now lets look at Walt's solution.
3,11,22,33,44,55 with magic number 333
(4) 333
= 330+3 (because we have a 3)
= 33 x 10 + 3 (I have a 33 but not a 10 - umm?) ok lets try
= 33 x 11 - 33 + 3 because I do have an 11.
umm now I don't have two 33s, I can't just factorise out 33 because that will just take me back to the last step. umm- well, -33+3=30 maybe that will help.
= 33 x 11 - 30 I've used the 33 and the 11 so the numbers I have left are 3,22,44,and 55. Umm 55-25=30, and 22+3=25 that's good
= 33 x 11 - (55-25)
= 33 x 11 - (55 -(22+3)) That's right but I suppose I should clean it up a bit.
= 33 x 11 - (55 - 22 -3)
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Actually that is not quite what he was thinking, I just relooked at his answer (33*11-(55-22))+3=333
up to here it is the same
=33 x 11 - 33 + 3 I have used 33 and 11 and 3 so how do I make 33 out of 22,44 and 55. Umm 55-22 = 33
=33 x 11 -(55-22) +3



[size=150]And that is how these can be done. With practice they don't take long, but they can take a long time until you learn some techniques![/size]

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Here are the next ones (choose the one that is best suited to your ability level)
Rules:
You have to use some or all of the numbers to make the magic number. You are not allowed to use any of the numbers twice. (Unless one was written twice in the first place)
You can use brackets, +, -, x, or divide and that is it.

HARD ONE
2,3,6,6,8,50 and the magic number is 972

EASIER ONE (not done yet)
3,5,2,4 and the magic number is 40
Happy calculations.
29 Jan 2014
 #3
avatar+118691 
0
*
I also often find probability very difficult.
There are lots of helpful tools, like the ones I have shown you here, but as soon as the question is slightly different you need real insight to answer it correctly.
In other words, you can't just regurgitate the rules all the time like you can (to more of an extent) in many other areas of maths.
It has crossed my mind that we could have more general ongoing post/s that deal specifically with probability questions.
I might get up to it sometime. (I don't know if you would be able but maybe you would like to try)

Also, that mathisfun site appears to be really good. I often refer people to it. For all sorts of maths things. If you find stuff over there (or anywhere else) you can share it with us if you want to.
I like Pascal's triangle too. It is fun!

Now, let's look at your answers,

Jedithious:


This has always been an area of math I've lagged behind in, being for some reason daunted by it. But with your thorough explanation combined with that amazing link, that lag is suddenly no longer. I believe the answers to the other two are:

"In how many different ways can you arrange 9 blue blocks and 9 red blocks in a straight line?"
18! = 6,402,373,705,728,000
6,402,373,705,728,000/(9!) = 17,643,225,600
17,643,225,600/(9!) = 48,620 Totally correct.
I was a little confused at first because I didn't see that you had divided by 9! twice.
It would have looked better to someone trying to follow if you had done both at once, like this;
18!/(9!*9!) and then just gone to the answer.

"In how many different ways can you arrange 25 blue blocks and 25 red blocks in a straight line?"
50! = 30,414,093,201,713,376,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
30,414,093,201,713,376,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000/(25!) = 1,960,781,468,160,819,281,929,913,523,584,869,531,669.8921948310508777
1,960,781,468,160,819,281,929,913,523,584,869,531,669.8921948310508777/(25!) = 126,410,606,437,751.9912453104638169556
Now tell me please, how can you arrange 50 things in anything other than a WHOLE number of ways!
You answer doesn't make sense. It is very close to correct, I think your calculator did something funny, oh, I see, you used the calc on this site. It does some funny stuff sometimes.
There is an excellent online calculator that i suggest you use, I have already set it up with this answer.
http://www.wolframalpha.com/input/?i=50%21%2F%2825%21*25%21%29&lk=4&num=1&lk=4&num=1
Again a nicer presentation would just be
50!/(25!*25!)
Another thing, when you write really big, or really tiny, numbers it is a good idea to present them in scientific notation, For someone like me, who is used to it, it is much easier to interprete the size of the answer. (My eyes aren't great either so counting all the digits can be a problem.) You did put in the commas, that made it much easier.
Thank-you

P.S. That entire site is really delightful. I especially like the Pascals Triangle section.

29 Jan 2014