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Math Fun #1165841
10/13/18 06:21 PM
10/13/18 06:21 PM
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-1. The economy of Roo Island is rather strange. They have four coins, each worth a different number of Neopoints. Three red coins plus two Neopoints equal a green coin. Three green coins plus five Neopoints equal a purple coin. Eleven red coins plus a single Neopoint equal a purple coin.

The fourth coin is a silver coin that is worth four purple coins. If I go to the Roo Island bakery and buy a loaf of bread worth 84 Neopoints with my silver coin, and the shopkeeper gives me change in red coins... how many red coins would I get?

-2. How can you draw a square with only 3 straight lines?

-3. What 3-digit number is described below?

If my three were a four
And my one were a three
What I am would be nine less
Than half what I'd be

-4. A bug starts out on the inside of a box that is 3 by 4 by 5. He is at height 1 from the base and distance 1 from the nearest corner along the side of length 4 (up along the side facing you). He wants to get to the corner diagonally opposite from his nearest corner at the base of the box. He cannot lose contact with the inside surface. What is the length of his shortest path?







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Re: Math Fun [Re: Pandora] #1165858
10/13/18 08:16 PM
10/13/18 08:16 PM
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Three red coins plus two Neopoints equal a green coin.
3r + 2 = g : g - 3r = 2 [1]

Three green coins plus five Neopoints equal a purple coin.
3g + 5 = p : -3g + p = 5 [2]

Eleven red coins plus a single Neopoint equal a purple coin.
11r + 1 = p : 11r - p = -1 [3]

The fourth coin is a silver coin that is worth four purple coins.
s = 4p [4]

Solving [1], [2] and [3] (3 unknowns, 3 equations) results in:
r = 5, g = 17 and p = 56

[4]: s = 4 * 56 = 224

If I go to the Roo Island bakery and buy a loaf of bread worth
84 Neopoints with my silver coin, and the shopkeeper gives me
change in red coins... how many red coins would I get?
s - 84 = 224 - 84 = 140
140 / 5 = 28 = number of red coins you'll get.


I'm a man of few words, BUT I use 'em often!!
Re: Math Fun [Re: Pandora] #1165871
10/13/18 09:52 PM
10/13/18 09:52 PM
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Well done, Denis. wave


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Re: Math Fun [Re: Pandora] #1165884
10/14/18 03:25 AM
10/14/18 03:25 AM
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2. Draw it at the edge of the sheet of paper, so that the edge provides the fourth side of the square (or is that cheating?). smile


Life is what happens while you're making other plans.

Re: Math Fun [Re: Pandora] #1165893
10/14/18 04:51 AM
10/14/18 04:51 AM
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4. If I'm interpreting the bug's location correctly,
I think the shortest path is 3*sqrt(5).

Re: Math Fun [Re: Pandora] #1165896
10/14/18 05:47 AM
10/14/18 05:47 AM
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4. I'll have a go at sqrt (7^2 + 5^2) = 8.6 think


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I wonder what's on television...?
Re: Math Fun [Re: Pandora] #1165905
10/14/18 09:03 AM
10/14/18 09:03 AM
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No correct answer yet. If the box wasn't see-through, the bug would be visible on the end flap facing you. Hope this helps. evil


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Re: Math Fun [Re: Pandora] #1165906
10/14/18 09:05 AM
10/14/18 09:05 AM
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2: expanding on Lex's sheet of paper:
can be done with 2 straight lines!

On #4:
"He is at height 1 from the base and distance 1 from the nearest
corner along the side of length 4 (up along the side facing you)"

That seems impossible: a diagonal is required from the "x" to the
nearest corner, which has to be greater than 1, since height = 1.
What am I missing?

Anyhoooo...bug travels directly to bottom: that's 1.
Then travels directly to far corner: path is hypotenuse
of right triangle with legs 3 and 5, so sqrt(3^2 + 5^2) = ~5.83
So total = 1 + 5.83 = 6.83 : a bit longer than CC's 3sqrt(5) = ~6.71


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Re: Math Fun [Re: Pandora] #1165910
10/14/18 09:44 AM
10/14/18 09:44 AM
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Gaaah! CCb was right! I miscalculated 3*sqrt(5) in my head.

It's easiest to lay the end of the box out flat, as shown below.



The bug travels the hypotenuse of a right triangle with legs of 3 and 6.


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Re: Math Fun [Re: Pandora] #1165915
10/14/18 09:52 AM
10/14/18 09:52 AM
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So the bug being 1 from the corner is not correct;
should be 1 from the side...right?

Ashamed to say that, my spatial vision being terrible,
I massacred a cereal box to build a replica crazy


I'm a man of few words, BUT I use 'em often!!
Re: Math Fun [Re: Pandora] #1165951
10/14/18 01:24 PM
10/14/18 01:24 PM
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Quote:
He is at height 1 from the base and distance 1 from the nearest corner along the side of length 4


He is where I marked the little x.

Great use of the cereal box! smile


Netflix needs to stop asking if I'm still watching and start asking if I've switched the laundry over yet
Re: Math Fun [Re: Pandora] #1165953
10/14/18 01:31 PM
10/14/18 01:31 PM
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2. Draw a square and put only 3 straight lines in it! lol


The best math you can learn is how to calculate the future cost of current decisions.
Re: Math Fun [Re: Pandora] #1165956
10/14/18 02:16 PM
10/14/18 02:16 PM
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#3. 4 possibilities; n = missing digit:

1: 13n -> 34n [1]
2: 1n3 -> 3n4 [2]
3: 31n -> 43n [3]
4: 3n1 -> 4n3 *
5: n13 -> n34 [4]
6: n31 -> n43 *
* these 2 are eliminated (division by 2)

[1] 130 + n + 9 = (340 + n)/2 : n = 62
[2] 100 + 10n + 3 + 9 = (300 + 10n + 4)/2 : n = 8
[3] 310 + n + 9 = (430 + n)/2 : n = -208
[4] 100n + 13 + 9 = (100n + 34)/2) : n = -1/10

So [2] is da winnah: 183
183 + 9 = 192 : 384/2 = 192

This has gotta be the most "fun" algebra problem I've seen!!


I'm a man of few words, BUT I use 'em often!!
Re: Math Fun [Re: Pandora] #1165957
10/14/18 02:39 PM
10/14/18 02:39 PM
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Sherlock lol

Denis, well done! wave


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Re: Math Fun [Re: Pandora] #1166017
10/15/18 01:50 AM
10/15/18 01:50 AM
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2. draw a square and then draw 3 lines inside it think


Sometimes lost is where you need to be. Just because you don't know your direction doesn't mean you don't have one.
Re: Math Fun [Re: Pandora] #1166041
10/15/18 09:03 AM
10/15/18 09:03 AM
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Nope, that's what Sherlock suggested. I will admit that this one is worded sneakily. grin


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Re: Math Fun [Re: Pandora] #1166044
10/15/18 09:48 AM
10/15/18 09:48 AM
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one of the lines is not quite straight?


I'm a man of few words, BUT I use 'em often!!
Re: Math Fun [Re: Sherlock] #1166051
10/15/18 10:38 AM
10/15/18 10:38 AM
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Hi Sherlock, great minds think alike wink


Sometimes lost is where you need to be. Just because you don't know your direction doesn't mean you don't have one.
Re: Math Fun [Re: Pandora] #1166061
10/15/18 11:54 AM
10/15/18 11:54 AM
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Code:
 
 _
|_| | | |

square with 3 straight lines


I'm a man of few words, BUT I use 'em often!!
Re: Math Fun [Re: Pandora] #1166069
10/15/18 01:18 PM
10/15/18 01:18 PM
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I was wondering about a sneaky capital A to the power of 2 (therefore squared) smile

Last edited by Lex; 10/15/18 01:22 PM.

Life is what happens while you're making other plans.

Re: Math Fun [Re: Pandora] #1166074
10/15/18 01:56 PM
10/15/18 01:56 PM
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I have a really great hint for you but I'm loving the group think tank too much. I'll post my hint tonight if nobody solves it first. You're so close! grin


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Re: Math Fun [Re: Pandora] #1166077
10/15/18 02:08 PM
10/15/18 02:08 PM
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You are cooking a date square and you draw it
out of the oven using a 3-prong fork lol


I'm a man of few words, BUT I use 'em often!!
Re: Math Fun [Re: Pandora] #1166112
10/15/18 08:05 PM
10/15/18 08:05 PM
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Hint time! And Lex already touched on it.

There's more than one kind of square in math. smile

Denis, very creative, but not correct. smile


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Re: Math Fun [Re: Pandora] #1166113
10/15/18 08:18 PM
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4 kissy


Sometimes lost is where you need to be. Just because you don't know your direction doesn't mean you don't have one.
Re: Math Fun [Re: Pandora] #1166120
10/15/18 08:51 PM
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Nailed it! kissy

(I hear the sound of palms slapping foreheads lol )


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Re: Math Fun [Re: Pandora] #1166133
10/15/18 10:23 PM
10/15/18 10:23 PM
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VERY cute puzzle!


I'm a man of few words, BUT I use 'em often!!
Re: Math Fun [Re: Pandora] #1166163
10/16/18 08:56 AM
10/16/18 08:56 AM
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CanukDenis Offline
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Another solution: 1 (1^2 = 1)


I'm a man of few words, BUT I use 'em often!!
Re: Math Fun [Re: Pandora] #1166232
10/16/18 06:55 PM
10/16/18 06:55 PM
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|\/ = 4 and |X = 9 and [ = 100


I'm a man of few words, BUT I use 'em often!!
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