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Mathematics Brain Teasers.


danydandan

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105 ?

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19 minutes ago, Habitat said:

105 ?

Yeap. 

Your turn to set a question.

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Not exactly a maths brain teaser, but what is the maximum number of different valid spellings  you can find for a word that is pronounced the same, but spelled differently. Homophones. For example "bear" and "bare", same sound, different spelling. The number of letters need not be the same, as with "bow" and "bough". The most I can come up with, is four, that have different spelling, but sound the exact same. I very much doubt there would be more than that, but there may be another group of 4, to the one I have in mind.

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3 hours ago, Habitat said:

Not exactly a maths brain teaser, but what is the maximum number of different valid spellings  you can find for a word that is pronounced the same, but spelled differently. Homophones. For example "bear" and "bare", same sound, different spelling. The number of letters need not be the same, as with "bow" and "bough". The most I can come up with, is four, that have different spelling, but sound the exact same. I very much doubt there would be more than that, but there may be another group of 4, to the one I have in mind.

Can we keep it strictly mathematically based please Hab. Thanks.

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Are we done, then?

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I'll stick another up. Soon

Or you can if you wish.

Edited by danydandan
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@Habitat do you want to set another teaser. 

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15 minutes ago, danydandan said:

@Habitat do you want to set another teaser. 

Can't think of one at the minute.

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4 minutes ago, Habitat said:

Can't think of one at the minute.

Ill pop one up tomorrow, if you think of one you can post it up. Thanks for participating.

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On 09/11/2018 at 8:17 AM, danydandan said:

Ill pop one up tomorrow, if you think of one you can post it up. Thanks for participating.

So, finally, we're done!?

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If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.

Is the above statement true, all the time!

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On 11/11/2018 at 7:25 AM, danydandan said:

If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.

Is the above statement true, all the time!

I've waited to let non-existent others have a go at this relatively easy question.

As usual, the answer depends on the geometric context. There are many geometries.

The answer is, yes, the lines must meet at a point if they exist in a Euclidean 2-dimensional space as per our traditional school geometry.

But their are many other non-Euclidian geometries (projective, hyperbolic, spherical, etc) where parallel lines can meet and non-parallel lines never meet! In a 3-dimensional space, for example, two non-parallel lines may never meet (think about it). 

Edited by Ozymandias
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1 hour ago, Ozymandias said:

I've waited to let non-existent others have a go at this relatively easy question.

As usual, the answer depends on the geometric context. There are many geometries.

The answer is, yes, the lines must meet at a point if they exist in a Euclidean 2-dimensional space as per our traditional school geometry.

But their are many other non-Euclidian geometries (projective, hyperbolic, spherical, etc) where parallel lines can meet and non-parallel lines never meet! In a 3-dimensional space, for example, two non-parallel lines may never meet (think about it). 

Excellent!

Your turn

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Starting with the first three natural numbers (1, 2, 3) the following sequence is generated:-

1, 2, 3, 6, 11, 20, , 37, 68, 125, 230,  .......

What is the next number in the sequence?

Edited by Ozymandias
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19 hours ago, Ozymandias said:

Starting with the first three natural numbers (1, 2, 3) the following sequence is generated:-

1, 2, 3, 6, 11, 20, , 37, 68, 125, 230,  .......

What is the next number in the sequence?

423? 

1+2+3=6

2+3+6=11

3+6+11=20

6+11+20=37

11+20+37=68

20+37+68=125

37+68+125=230

68+125+230=423.

That's the pattern I've got anyways.

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Yes, Dan, you got it. 423 is the answer.

It's your turn again, if you want to continue. Personally, I'm disappointed with the lack of interest. Where are all the science people? There must be none on here with any maths ability, and nearly all of these 'teasers' can be attempted with second level/high school maths knowledge. 

Edited by Ozymandias
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11 minutes ago, Ozymandias said:

Yes, Dan, you got it. 423 is the answer.

It's your turn again, if you want to continue. Personally, I'm disappointed with the lack of interest. Where are all the science people? There must be none on here with any maths ability, and nearly all of these 'teasers' can be attempted with second level/high school maths knowledge. 

We both know it's our Irish education and it's obvious that people are not as smart as us Irish. Hehe.

I'll stick to the pattern and sequence concept.

Eh,,, ok.

11, 21, 35, x, 75.

What is x.

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On 11/13/2018 at 8:53 AM, danydandan said:

We both know it's our Irish education and it's obvious that people are not as smart as us Irish. Hehe.

I'll stick to the pattern and sequence concept.

Eh,,, ok.

11, 21, 35, x, 75.

What is x.

Nobody is going to answer this so I will, again:

11 + 10 = 21

21 + 14 = 35

35 + 18 = 53              so X = 53 

53 + 22 = 75

 

Edited by Ozymandias
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5 hours ago, Ozymandias said:

Nobody is going to answer this so I will, again:

11 + 10 = 21

21 + 14 = 35

35 + 18 = 53              so X = 53 

53 + 22 = 75

 

Yeap, sorry Ozy I thought I replied earlier. 

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Let's call it a day. Thanks for the thread. :tu: :)

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9 hours ago, Ozymandias said:

Let's call it a day. Thanks for the thread. :tu: :)

I'll keep posting anyways. Thanks for participating helped get me chemotherapy riddled brain working again.

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1 hour ago, danydandan said:

I'll keep posting anyways. Thanks for participating helped get me chemotherapy riddled brain working again.

Well, Dan, I just thought as it is your thread you might be thinking about wanting to stop due to no interest. I'm willing to continue if you are but there will be no pint either of us posing question to each other that come out of our own areas of expertise and employ advanced mathematical techniques. If we continue we should agree to keep the teasers relatively simple and always give a solution with a solution method that lurkers might like to see even if they don't feel confident to participate. I'm thinking second level school maths. 

PS - Sorry to hear that you seem to have had a major health issue. Do you mind if I ask what it was and how are you now?

Edited by Ozymandias
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13 minutes ago, Ozymandias said:

Well, Dan, I just thought as it is your thread you might be thinking about wanting to stop due to no interest. I'm willing to continue if you are but there will be no pint either of us posing question to each other that come out of our own areas of expertise and employ advanced mathematical techniques. If we continue we should agree to keep the teasers relatively simple and always give a solution with a solution method that lurkers might like to see even if they don't feel confident to participate. I'm thinking second level school maths. 

PS - Sorry to hear that you seem to have had a major health issue. Do you mind if I ask what it was and how are you now?

I'll keep to a pass level Text and Tests level so. Lol.

I'm going ok now, had cancer and all the crap that comes with it. Starting back at work after Christmas so I'm doing good thankfully. In all honesty my wife bor the brunt of it.

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1 hour ago, danydandan said:

I'll keep to a pass level Text and Tests level so. Lol.

I'm going ok now, had cancer and all the crap that comes with it. Starting back at work after Christmas so I'm doing good thankfully. In all honesty my wife bor the brunt of it.

Good to hear that, Dan, and, yes, the spouses have a lot to carry, as do the kids. It's great what they can do with cancer these days. Although it is a frightening and life changing disease they can cure most of them if caught early. 

PS - That level seems good to me. :)

Edited by Ozymandias
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In a given population 57% are female; 62% are unemployed; and 44% are at least 40 years old. What is the probability that any person randomly chosen from this population will be an employed male under 40 years of age?

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