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| eyn |
 Posted: Apr 07, 2006 11:10 am |
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羽ありたまご
Joined: 13 Apr 2005
Posts: 2094
Location: Canada
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Well, I think horizon180 is right, but here's my explanation.
You can buy 4, 5 and 6 nuggets. So let's try other number one by one.
7 - impossible
8 - 4 x 2
9 - 5 + 4
10 - 5 x 2
Take note that from this point onward, 10, 15, 20 will all be possible using 5 x N, where N is an integer.
11 - 6 + 5
12 - 6 x 2
13 - 4 x 2 + 5
From this point onward, we do not need to test if other numbers are possible anymore. Remember we can represent 10, 15 etc. using multiples of 5.
Say I want 14, I can use 14 = 10 + 4, and 10 is a multiple of 5.
15 itself is already a multiple of 5.
16 = 10 + 6
17 = 5 + 12 (we already proved 12)
18 = 10 + 8 (same as above)
19 = 15 + 4
20 (multiple of 5 again)
21 = 10 + 11
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You guys get the idea don't you? Now, how can I get 127? Okay, it's easy. 110 is multiple of 5. We need to add 17 which we have already prove to be possible. |
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| Jester |
| Posted: Apr 13, 2006 3:53 pm |
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フレンジャー
Joined: 27 Feb 2006
Posts: 843
Location: Canada
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Yeah, I agree. You both got it. Here's how I attacked this question.
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(1) 10 is easy to make so the problem is with the digits in the 'ones' position because I can add ten to any other number to get the correct number in the 'ten' and above positions.
>> 10 = 5 + 5
(2) 4, 5, 6, 7, 8 and 9 are easy too. Now we can make any numbers that end with 4, 5, 6, 7, 8, and 9 are easy.
>> 4, 5, 6 are given
>> 8 = 4 + 4
>> 9 = 4 + 5
>> 10n + 4 (any number ending in 4)
>> 10n + 5 (any number ending in 5)
>> 10n + 6 (any number ending in 6)
>> 10n + 8 (any number ending in 7)
>> 10n + 9 (any number ending in 9)
>> n = 0,1,2,3,4...
(3) Now because 1,2, and 3 are impossible we have to resort to 11, 12, 13, and 17 because the digit in their 'ones' place is 1, 2, and 3 respectively.
>> 11 = 5 + 6
>> 12 = 6 + 6
>> 13 = 5 + 4 + 4
>> 17 = 5 + 6 + 6
>> 10n + 11 (almost any number ending in 1) (1 isn't possible)
>> 10n + 12 (almost any number ending in 2) (2 isn't possible)
>> 10n + 13 (almost any number ending in 3) (3 isn't possible)
>> 10n + 17 (almost any number ending in 7) (7 isn't possible)
>> n = 0,1,2,3,4...
(4) Therefore, only 1, 2, 3, and 7 can't be made. 7 is the largest number of nuggets that a customer cannot order, but I'm sure those friendly employees could sneak you an extra for your 6 pack.
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This one honestly took me a lot longer then I thought. Awesome question!
Note: This question cost me precious exam studying time. Thank you. |
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| kikubelle |
| Posted: Apr 14, 2006 8:01 pm |
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ユメクイ
Joined: 27 Jul 2005
Posts: 1026
Location: Toronto, Canada + Lalaland~
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good job horizon, eyn and Jester
you got it hahaXD
someone put up another one!  |
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| Jester |
| Posted: Apr 15, 2006 12:33 am |
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フレンジャー
Joined: 27 Feb 2006
Posts: 843
Location: Canada
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I think our brains need a breather after that noggin-scratching math questions. Here's a simpler riddle that I really like. Have fun! What phrase is represented by the image below:
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| horizon180 |
| Posted: Apr 15, 2006 11:27 am |
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SMILY
Joined: 26 Oct 2005
Posts: 495
Location: Manchester, UK
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erm...
foot in mouth? you know, putting ones foot in one's mouth... saying something that you regret saying as soon as you say it...
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| Jester |
| Posted: Apr 15, 2006 12:19 pm |
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フレンジャー
Joined: 27 Feb 2006
Posts: 843
Location: Canada
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Haha, that's a negative horizon180. Keep tryin' though.  |
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| flintandtas |
| Posted: Aug 04, 2009 7:03 am |
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クラゲ, 流れ星
Joined: 07 Jul 2009
Posts: 8414
Location: Sydney, Australia
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Just browsing through and saw this old thread and couldn't help myself ... tiptoe through the tulips? or should that be chulips?
OK, I'm no good at thinking up riddles, so I'll post the only one I can think of which is really simple and I'm sure you heard before ...
What is it that the more you take out, the bigger it gets?
^ this better take less than 3 years to solve  |
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| Crystallas |
| Posted: Aug 04, 2009 8:52 am |
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クラゲ, 流れ星
Joined: 29 Apr 2008
Posts: 10763
Location: Germany
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^ This is easy, a hole  !
Ok, a new one:
Samuel was out for a walk when it started to rain. He did not have an umbrella and he wasn't wearing a hat. His clothes were soaked, yet not a single hair on his head got wet. How could this happen?
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| Yunchen |
| Posted: Aug 04, 2009 8:55 am |
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恋愛写真
Joined: 27 Oct 2005
Posts: 1242
Location: Germany
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| ^ uhm....he's bald? |
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| Crystallas |
| Posted: Aug 04, 2009 9:04 am |
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クラゲ, 流れ星
Joined: 29 Apr 2008
Posts: 10763
Location: Germany
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| ^ You got the right answer Yunchen |
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| Yunchen |
| Posted: Aug 04, 2009 3:50 pm |
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恋愛写真
Joined: 27 Oct 2005
Posts: 1242
Location: Germany
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yay!
ok...I don't really know many riddles...but one comes to my mind since my former math teacher used it as a bonus question in one of our exams don't expect much, though XD
Peter's father has three sons. Their names are Huey, Dewey and...? |
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| Koda |
| Posted: Aug 04, 2009 4:43 pm |
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クラゲ, 流れ星
Joined: 27 Oct 2008
Posts: 12318
Location: Still on Mars
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Huey, Dewey and Peter 
so, riddle me this! What can run but never walks, has a mouth but never talks, has a head but never weeps, has a bed but never sleeps? |
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| flintandtas |
| Posted: Aug 05, 2009 3:09 am |
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クラゲ, 流れ星
Joined: 07 Jul 2009
Posts: 8414
Location: Sydney, Australia
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I've been scratching my head all day thinking about this and its finally come to me ... the answer is a river!
OK, now Yunchen asked us
Peter's father has three sons. Their names are Huey, Dewey and...?
Koda claims that the answer is Huey, Dewey and Peter.
But I know from a very reliable source that the three sons are really Huey, Dewey and Louie.
Now my riddle be, why am I not wrong? |
Last edited by flintandtas on Aug 12, 2009 3:22 am; edited 1 time in total |
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| flintandtas |
| Posted: Aug 12, 2009 3:21 am |
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クラゲ, 流れ星
Joined: 07 Jul 2009
Posts: 8414
Location: Sydney, Australia
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No answer for this as well in a while so clue time it be:
Huey has only two brothers, Dewey and Louie? |
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| Yunchen |
| Posted: Aug 12, 2009 5:13 am |
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恋愛写真
Joined: 27 Oct 2005
Posts: 1242
Location: Germany
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| ^ Peter is a girl with an unconventional name? |
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