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Thread: A mixed bunch

20041220, 11:57 #1
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A mixed bunch
1) The number is secret, it has 3 digits.
a) The sum of the 3 digits multiplied by 36 equals the secret number
[img]/forums/images/smilies/cool.gif[/img] If you multiply the first digit by 7 and then add 9 you will get the same as the sum of the two other digits multiplied by 5.
c) If you multiply the second digit with 8 and then take away 9 you will get the same number as the sum of the first and third digits.
What is the secret number?
2) 48 is a special number.
a) If you add 1 to it you get a square (7x7=49)
[img]/forums/images/smilies/cool.gif[/img] If you add 1 to half of 48 you get 25 which is also a square (5x5=25)
What is the next number which this rule applies?
3) After you burn a candle, you get a stub. By using 6 stubs, you can make a candle. You have 1001 stubs, how many new candles can you make?Jerry

20041220, 12:13 #2
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Re: A mixed bunch
2. <span style="backgroundcolor: #FFFF00; color: #FFFF00; fontweight: bold">1680: 1681 = 41*41 and 841 = 29*29.</span hide>

20041220, 12:20 #3
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Re: A mixed bunch
3. <span style="backgroundcolor: #FFFF00; color: #FFFF00; fontweight: bold">200:
Use 996 stubs to make 166 candles; 5 stubs left over.
Burn the 166 candles. You now have 166+5 = 171 stubs.
Use 168 stubs to make 28 candles; 3 stubs left over.
Burn the 28 candles. You now have 28+3 = 31 stubs.
Use 30 stubs to make 5 candles; 1 stub left over.
Burn the 5 candles. You now have 5+1 = 6 stubs.
Use the 6 stubs to make 1 candle.
(If you burn the last one, you have just one stub. Not enough to make more candles.)
Total made: 166+28+5+1 = 200.</span hide>

20041220, 12:21 #4
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Re: A mixed bunch
Well done Hans 2 and 3 correct
Jerry

20041220, 12:26 #5
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Re: A mixed bunch
1. <span style="backgroundcolor: #FFFF00; color: #FFFF00; fontweight: bold">324
9*(3+2+4) = 9*36 = 324
7*3+9 = (2+4)*5
8*29 = 3+4</span hide>

20041220, 12:28 #6
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Re: A mixed bunch
Well done again.
My scratch pad got a good scribbling on this morning!Jerry

20041220, 12:37 #7
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Re: A mixed bunch
OK Hans
What is the next one.Jerry

20041220, 12:48 #8
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Re: A mixed bunch
The next ones are <span style="backgroundcolor: #FFFF00; color: #FFFF00; fontweight: bold">57120, 1940448 and 65918160.</span hide>

20041220, 14:12 #9
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Re: A mixed bunch
I doff my cap to you sir.
I did it in Excel, what was your secret, scratch pad or VB?Jerry

20041220, 15:18 #10
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Re: A mixed bunch
I solved 1 and 3 with pen and paper, and used a VBA macro to solve 2 (it happened to be in Excel, but it could have been any application with VBA).

20041221, 11:30 #11
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Re: A mixed bunch
I tried to have a go at 2. using diophantine equations (which I know very little about). Such an equation would be of the form:
y