Xmas 2018 Puzzle (1)

L D[AR2P#0.0]

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Nov 2006
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I came across this old chestnut recently and thought I'd post it.


A PLC project involving structured text (ST), function block diagram (FBD) and statement list (IL) has been
quoted at 1000 hours. There are a total of 100 blocks in the project and the time to code and test each type of block is as follows:
ST = 50 hours
FBD = 10 hours
IL = 0.5 hours.

How many of each type of block are there?

Answers by PM with reasoning please - don't bother with brute force solutions.
 
Solution:


S+f+I=100
50S+10f+0.5I=1000
S,f,I are whole numbers
S,f,I greater than 0 and less than 99

Double second eqn..
100S+20f+I=2000
Sub first eqn from this
99S+19f=1900
Rearrange
S=19(100-f)/99
For S to be a whole number, (100-f) must be a multiple of 99. Zero doesn't count as the problem states "does contain ST"
f=1
S=19
I=80
 

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