Gifted Mathematics - Latest Comments

Re: Gifted Mathematics: Paths on a Cube: Lower Secondary Mathematics Competition Question

Al Jaques — Tue, 23 Apr 2013 00:06:19 -0000

The overall structure is not a cube. Just sayin'.

Re: Gifted Mathematics: The Sylver Coinage Game: Upper Secondary Mathematics

rychardemanne — Thu, 18 Apr 2013 21:36:01 -0000

When I started looking at this game, it was off the back of the coin problem and Frobenius number. There is a js calculator that will do the same thing as the CDF, without the freaky behaviour.

http://mathsjavascript.free...

It too, is limited to gcd=1, but it is not limited in the size of the input numbers. It also calculates all the numbers that are not linear combinations of the inputs. So at the start, I used this to play the game numerically. Hope this helps.

As before, if anybody knows of better calculators, espcally tose that accept gcd>1 then please let everybody know :-)

Re: Gifted Mathematics: The Sylver Coinage Game: Upper Secondary Mathematics

rychardemanne — Thu, 18 Apr 2013 20:12:32 -0000

having said all that, there are enough links to know how to calculate the remaining numbers, at least for low number games. Finding the highest number that cannot be made as a linear combination of positive numbers and positive integral coefficients was part of an earlier question this week.

Re: Gifted Mathematics: The Sylver Coinage Game: Upper Secondary Mathematics

rychardemanne — Thu, 18 Apr 2013 20:08:40 -0000

Hi, Kevin, at the bottom of the CDF page it does mention that it limits the game to gcd=1. The two games above, {5,7} and {7,9} it works because both starting numbers are coprime, but for the PMQ that's coming up... it will help a little, but not a lot.

The freaky part is, for example, clicking the 9 and seeing all the multiples of 3 disappear - this should NOT happen, only the multiples of 9 should be out of the game. But once you click another number, say the 7, the new calclation is fine and it frees up the 3 and 6 and so on. So it behaves oddly to force only gcd=1 opening first two moves.

As the source code is open source, does anybody fancy a project to actually make it play a more realistic game?

Re: Gifted Mathematics: The Sylver Coinage Game: Upper Secondary Mathematics

Kevin O'Bryant — Thu, 18 Apr 2013 13:10:25 -0000

rychardemanne is correct, the CDF is flawed and does not play Sylver Coinage. It is unclear to me the rules being used there.

Re: Gifted Mathematics: The Sylver Coinage Game: Upper Secondary Mathematics

rychardemanne — Thu, 18 Apr 2013 07:58:21 -0000

Has anybody used the CDF on Wolfram? Note that there is a limitation in that you can only play numbers 2-20. However, there also appears to be a bug in it!

If you play any even number, it blocks out all even numbers. This is not how the game works. If you click 8 then all multiples of 8 are out of the game, but other even numbers should still be available. If you then click any remaining odd numbers the list of available numbers recalculates correctly.

In essence, this means you have to play a bounded game immediately. It is still useful in learning how the game works but limits the number of interesting games.

Re: Gifted Mathematics: Dissecting a Cube: Upper Secondary Mathematics Competition Question

Guest — Thu, 11 Apr 2013 01:20:52 -0000

26 (3x3cubed + 3x2cubed + 20singles)

Re: Gifted Mathematics: Prize Maths Quiz: A Triangular Tiling Puzzle (PMQ13)

rychardemanne — Mon, 08 Apr 2013 04:59:17 -0000

Just over 12 hours to go on this PMQ and no correct answers yet.

If no winners, I will leave this open as a project, so feel free to ask questions.

One hint: the size of the large triangle is 39, so the obvious place to start is with the two largest possible inner triangles. These are of sizes 19 and 20 and, indeed, they are in the solution :-) Now you just need to find the rest.

Re: Gifted Mathematics: Prize Maths Quiz: An 18-Sided Polygon (PMQ12)

rychardemanne — Mon, 01 Apr 2013 21:34:18 -0000

This PMQ has now closed, so feel free to comment about the question and discuss your answer.

Re: Gifted Mathematics: A Cross-Number Puzzle: Upper Primary Mathematics Competition Question

Graeme McRae — Mon, 01 Apr 2013 17:43:48 -0000

To move quickly to a solution, my hint is that there are only 5 3-digit cubes: 125, 216, 343, 512, and 729.

Re: Gifted Mathematics: This is hard!: Upper Primary Mathematics Competition Question

Terence Fagan — Sun, 31 Mar 2013 23:38:53 -0000

Here is what I have so far, it is late so I am heading to bed.

Single Solution T+1 = H

Single Solution H+1 = A

Model 1 ->

2I = 1R

è
2S = D

Model 2 ->

2I +1 = 1R

-> 2S =1D

According to this model.

H = 9

T = 8

A = 0

Model 1

If I = 6

-> R = 2

-> and if S = 1

-> D = 2 (Not Valid)

If I =7

-> R=4

-> and if S = 2

->D = 4
(Not Valid)

-> and if S = 1

->D = 2
Valid

Model 2

If I = 6

-> R=3

and if

Final Number

1. 80_ _ Keep iterating

2. 8012

Re: Gifted Mathematics: Feynman Point Poems - Join In - Write Your Own!

rychardemanne — Sun, 31 Mar 2013 02:30:06 -0000

That's very good, thanks!

Re: Gifted Mathematics: Feynman Point Poems - Join In - Write Your Own!

Jon Ziegler — Sat, 30 Mar 2013 20:37:15 -0000

And relevant to the other topic at hand:
Feynmanic condition:
Brilliant, inspiring physicist
manifests.

Re: Gifted Mathematics: Feynman Point Poems - Join In - Write Your Own!

Jon Ziegler — Sat, 30 Mar 2013 19:52:22 -0000

And another on the topic of pi...

Continued fractions expansion
Converges perfectly...
Pi-licious!

Re: Gifted Mathematics: Feynman Point Poems - Join In - Write Your Own!

Jon Ziegler — Sat, 30 Mar 2013 19:50:27 -0000

In the spirit of staying on topic, here's one titled "Pi". See http://neilbickford.com/pic... for an explanation if needed.
Pi
--
Audacious alternate expansion:
Continued fractions!
Gosperize!

Re: Gifted Mathematics: Feynman Point Poems - Join In - Write Your Own!

Jon Ziegler — Sat, 30 Mar 2013 19:00:04 -0000

Fortunate chocolate consumers:
Fantastic! Delicious! Marvelous!

Re: Gifted Mathematics: Feynman Point Poems - Join In - Write Your Own!

rychardemanne — Sat, 30 Mar 2013 04:53:43 -0000

I will add some entries from other websites and forums so people here can vote on them. I will obviously include a link to the original. First one is:

http://www.science20.com/co...

Crisis Telephone Counselling

Agonising sensation, isolation, confusion, imagining, suiciding :(

Answering, listening, grounding, exploring, imagining, rejoicing :)

Re: Gifted Mathematics: Feynman Point Poems - Join In - Write Your Own!

rychardemanne — Sat, 30 Mar 2013 04:44:43 -0000

Many thanks for a quick start!

Please note that you can vote each entry up or down using the arrows just below each comment.

Also, a reminder that this is usually a site for students and teachers, so keep it clean! If you wish to test out a more adults audience then try posting at the same article on Science 2.0

http://www.science20.com/fl...

Enjoy!

Re: Gifted Mathematics: Feynman Point Poems - Join In - Write Your Own!

Trent Boatner — Fri, 29 Mar 2013 18:52:14 -0000

AGNOSTICS

WILLINGLY

BLASHPEME;

PARENTING

ABANDONED

BISEXUALS.

Re: Gifted Mathematics: Feynman Point Poems - Join In - Write Your Own!

Tristan Axe — Fri, 29 Mar 2013 15:11:24 -0000

Abandoned bleakness chirruped dirgelike impromptu metaphors.

Re: Gifted Mathematics: Pool Table Trick Shot: Upper Secondary Mathematics Competition Question

zahed shah — Thu, 28 Mar 2013 15:26:32 -0000

75cm

Re: Gifted Mathematics: Prize Maths Quiz: A Binary Message (PMQ11)

rychardemanne — Mon, 25 Mar 2013 21:24:16 -0000

Hi, the answer is higher than 39.
A technique is to rewrite each sequence in terms of the lengths of subsequences. Eg 10110001 -> 11231. How many combinations are there of three 1s one 2 and one 3? Make a list of all such sequences and add the combinations.
The list is not very long but you must be careful to include all possibilities.

Let me know how you get on.

Re: Gifted Mathematics: Prize Maths Quiz: A Binary Message (PMQ11)

rychardemanne — Mon, 25 Mar 2013 21:15:03 -0000

OK, this PMQ has closed! You are free to discuss the answer.

Re: Gifted Mathematics: Prize Maths Quiz: A Binary Message (PMQ11)

Vineet — Sun, 24 Mar 2013 02:49:08 -0000

The valid message which can be formed out of 10 bits will be 1110001110
now let us consider the bits within the bracket (11100)01110
The possible combination of bits which can be formed and satisfy as valid message will be 5C3
now let us consider the bits within the bracket 1110(001110)
The possible combination of bits which can be formed and satisfy as valid message will be 6C3
now let us consider the bits within the bracket (1110)0(01110)
The possible combination of bits which can be formed and satisfy as valid message will be 4C3 x 5C3

The total valid message which can be formed will be
5C3 + (6C3-1) + (4C3-1) x (5C3-1)

I hope the answer will be right.

Re: Gifted Mathematics: Prize Maths Quiz: A Binary Message (PMQ11)

Vineet George — Fri, 22 Mar 2013 07:11:35 -0000

I think the answer is 39