Question 767124
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The only way to do this is to start with one of the lengths and see what is possible.  You have to go 5 meters which is 500 cm, so


9 times 60 is 540.  9 60s is too many,


8 times 60 is 480.  You don't have a 20 cm piece, so this doesn't work


7 times 60 is 420.  No way to make 80 out of 70 and 100, so this doesn't work.


6 times 60 is 360.  500 minus 360 is 140 which you can make with two 70s.


5 times 60 is 300.  500 minus 300 is 200 which you can make with two 100s.


4 times 60 is 240.  No way to get to 260 with just 70s and 100s, so this doesn't work.


3 times 60 is 180.  Leaves 320, and you can't get there from here either without using 60s and that possibility is already counted above.


2 times 60 is 120.  Leaves 380.  4 70s is 280 plus one 100 makes 380.


1 times 60 is 60.   Leaves 440.  2 times 70 is 140 plus 3 times 100.


0 times 60.  Leaves 500 which is just five 100s.


In sum:


5 100s
3 100s plus 2 70s plus 1 60
1 100 plus 4 70s plus 2 60s
2 100s plus 5 60s
2 70s plus 6 60s


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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