Math Fun
#1165841
10/13/18 06:21 PM
10/13/18 06:21 PM
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Joined: Aug 2000
Posts: 52,987 Upstate NY
Pandora
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Sonic Boomer
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OP
Sonic Boomer
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Posts: 52,987
Upstate NY
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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?
The moon is actually more useful than the sun since the moon gives us light at night when it's dark. The sun only gives us light during the day when it's already bright out.
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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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Joined: Nov 2000
Posts: 18,719 Ottawa Ontario Canada
CanukDenis
Graduate Boomer
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Graduate Boomer
Joined: Nov 2000
Posts: 18,719
Ottawa Ontario Canada
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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!!
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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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Joined: Nov 2000
Posts: 18,719 Ottawa Ontario Canada
CanukDenis
Graduate Boomer
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Graduate Boomer
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Posts: 18,719
Ottawa Ontario Canada
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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
I'm a man of few words, BUT I use 'em often!!
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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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Joined: Aug 2000
Posts: 52,987 Upstate NY
Pandora
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OP
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Upstate NY
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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.
The moon is actually more useful than the sun since the moon gives us light at night when it's dark. The sun only gives us light during the day when it's already bright out.
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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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Joined: Nov 2000
Posts: 18,719 Ottawa Ontario Canada
CanukDenis
Graduate Boomer
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Graduate Boomer
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Posts: 18,719
Ottawa Ontario Canada
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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
I'm a man of few words, BUT I use 'em often!!
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Re: Math Fun
[Re: Pandora]
#1165951
10/14/18 01:24 PM
10/14/18 01:24 PM
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Joined: Aug 2000
Posts: 52,987 Upstate NY
Pandora
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OP
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Upstate NY
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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!
The moon is actually more useful than the sun since the moon gives us light at night when it's dark. The sun only gives us light during the day when it's already bright out.
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Re: Math Fun
[Re: Pandora]
#1165956
10/14/18 02:16 PM
10/14/18 02:16 PM
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Joined: Nov 2000
Posts: 18,719 Ottawa Ontario Canada
CanukDenis
Graduate Boomer
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Graduate Boomer
Joined: Nov 2000
Posts: 18,719
Ottawa Ontario Canada
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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!!
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Re: Math Fun
[Re: Pandora]
#1166069
10/15/18 01:18 PM
10/15/18 01:18 PM
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Joined: Mar 2004
Posts: 11,891 Isle of Man
Lex
Adept Boomer
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Adept Boomer
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Isle of Man
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I was wondering about a sneaky capital A to the power of 2 (therefore squared)
Last edited by Lex; 10/15/18 01:22 PM.
Life is what happens while you're making other plans.
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Re: Math Fun
[Re: Pandora]
#1166112
10/15/18 08:05 PM
10/15/18 08:05 PM
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Joined: Aug 2000
Posts: 52,987 Upstate NY
Pandora
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Sonic Boomer
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OP
Sonic Boomer
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Posts: 52,987
Upstate NY
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Hint time! And Lex already touched on it. There's more than one kind of square in math. Denis, very creative, but not correct.
The moon is actually more useful than the sun since the moon gives us light at night when it's dark. The sun only gives us light during the day when it's already bright out.
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Re: Math Fun
[Re: Pandora]
#1166120
10/15/18 08:51 PM
10/15/18 08:51 PM
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Joined: Aug 2000
Posts: 52,987 Upstate NY
Pandora
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Sonic Boomer
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OP
Sonic Boomer
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Posts: 52,987
Upstate NY
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Nailed it! (I hear the sound of palms slapping foreheads )
The moon is actually more useful than the sun since the moon gives us light at night when it's dark. The sun only gives us light during the day when it's already bright out.
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