 # Thread: Programming Puzzle 1 - Simple Loop

1. ## Re: Programming Puzzle 1 - Simple Loop

Very nice, Thomas.

The message board left justifies your script. That makes it harder to read scripts because we lose the indents.

Code:
```option strict

dim target_num as n = 0 'used to determine if number is even
dim i as n = 0
dim result as n = 0 'result adds the total of the even numbers
dim num_loops as n = 0 'counts the number of interations

for i = 302 to 101 step-2
num_loops = num_loops + 1
target_num = i
if mod(target_num,2)= 0 then
result=result+target_num
end if
next i

ui_msg_box("Program Puzzle One","The answeres are Sum = "+ alltrim(str(result))+" Loops = "+alltrim(str(num_loops)))

end```
The # button on the advanced editor toolbar will do this for you. Just select the text to be encapsulated, and click #.

Also, when you develop a solution to the next puzzle, I suggest you learn how to "export" your script as a text file, and then simply attach it to a reply here. If you use the script export tool in Alpha Five the text file will be specially formatted to work with Alpha's import tool. This makes it easier for us to study your code and run it on our machines. We just import your previously exported script. To get to the export (and import) tools, save your script to the Code page of the A5 control panel. Then right click the script name. Choose Export off the drop down list (context menu).

Welcome to the board! 2. ## Re: Programming Puzzle 1 - Simple Loop

Just came across this part of the message board. Not sure whose idea it is to have a section for "Puzzles"..but I think it's a pretty good idea..
On to the first puzzle..don't have time to scan over any others..nor to scan over the responses, but this puzzle, clearly, can be solved without any loops whatsoever, rather with one simple expression. But if I do that then I am in violation of the rules.
For those who might be interested, here is the expression:
Code:
`vtotal=int((end-start)/2)+1+(int((end-start)/2)+1)*if(mod(start,2)=0,start-2,int(start/2)*2)+(int((end-start)/2)+1)^2`
Where vtotal is the sum of all even values, start is the bottom value and end is the top value, all inclusive.

If I want to be de facto in compliance with the rules, I could be a slick, clever, irritating smart alec, which I do not want to be, but again, for those who might be interest, I will use a single loop that does nothing and I will have my lawyer sue and demand the ultimate prize arguing that I am in full compliance with the rules the way they were written and offered.
Here is the smart alec script:
Code:
```option strict
dim start as n'this is the bottom value
dim end as n'this is the top value
dim i as n 'to be used as a counter in the loop
dim vtotal as n
start=101
end = 302
'Now we will use the same expression provided in the previous example and add a dummy loop
for i=1 to 1
vtotal=int((end-start)/2)+1+(int((end-start)/2)+1)*if(mod(start,2)=0,start-2,int(start/2)*2)+(int((end-start)/2)+1)^2
next
msgbox("The total sum is: "+vtotal+"  and the script used 1 loop")```
'The same could be done using while..end while loop
Code:
```option strict
dim start as n'this is the bottom value
dim end as n'this is the top value
dim i as n 'to be used as a counter in the loop
dim vtotal as n
start=101
end = 302

while i<=1
vtotal=int((end-start)/2)+1+(int((end-start)/2)+1)*if(mod(start,2)=0,start-2,int(start/2)*2)+(int((end-start)/2)+1)^2
i=i+1
end while
msgbox("The total sum is: "+vtotal+"  and the script used 1 loop")```
There is only one loop, about as few as you can get unless I hire the real smart alec lawyer who will argue for my original expression to be the ultimate winner as it has zero loops!! But I don't think the panel of judges will buy that.

As you can see, even if the judges accept the logic of zero loops or one loop, still I wont get any prizes since I am still in violation of the rules since I didn't explain how and why does that expression work, and I wont.. To understand this expression, you have to mentally translate this math puzzle into a geometric one..to explain that is a bit time consuming and outside the parameters of this puzzle, so we will move on to a more realistic solution, which I will start in a new post and and ask you to please ignore this post as a side show that may or may not have any redeeming value. 3. ## Re: Programming Puzzle 1 - Simple Loop

So, on to a more realistic solution, one that complies with the spirit rather than the letter of the rules.
My first instinct was to:
1-identify the first even number
2-Loop stepping by 2 adding the values until reach the top value.
I ended up with 100 loops. That's embarrassing! a hundred loop to solve a simple puzzle like this? There got to be a better way.
There is..
One that uses a 20 loops or few more.
Here it is:
P.S.: To best read the introduction in case your screen rsolution is different from mine, copy/paste it into Word and read it in Word.
Code:
```'Introduction:
'The object is to sum all even values between 2 given numbers
'Since these 2 numbers are provided in the puzzle, meaning I could hard-code these values which makes everything a lot simpler and faster but just in case the intent was to solve for any numbers not just the ones provided in the puzzle, the script is written so that you can substitute these number at will and get the correct result.
'
'To add all even values between 2 given numbers, you identify the first even number, then add 2 to it and add the new number to the previous one and so on..
'That's the standard way of thinking.. by doing that you will have to loop as many times as there are even values..
'That's too many loops and too expensive..
'
'Let's look at the puzzle from a different perspective..
'
'In the example provided, the first even number is 102.
'Let's call this number a base.
'Every subsequent number is 2 points more than the one before..
'Let's get away from this line of thinking.
'A different way to think about is:
'You have a base number, then
'Every subsequent number has one more 2 than the one before, i.e.:
'The base number is 102
'The one after has one more 2 than the base: 104
'The one after has two more 2's than the base: 106
'The one after has three more 2's than the base: 108
'and so on..
'
'Now if I strip the base of its 2, then we could re-state the above as follows:
'Instead of the base, I am going to have new figure, will call it the "denominator" which is the base stripped off its 2, i.e. 102-2=100
'
'Now the first even value (the base, 102) has one 2 more than the denominator and
'The second even value (104)  has two 2's more than the denominator
'The third even value (106) has three 2's more than the denominator
'and so on..
'
'so now I could deal with 2 sets of values:
'The first set, we will call it the "Denominator-cluster" is basically made up of the even values stripped off their 2's. meaning, they are all 100
'
'The second set, we will call it the "Two-cluster" is made up of those 2's that are above and beyond the denominator. This is a series made up as one 2, two 2's, three 2's... ten 2's.
'
'Now I am going to break up all the even values between 101 and 302 into 10 clusters.
'As you can see, the "Denominator-clusters" will each have 10 equal values. the first cluster will have 10 equal values each of 100. If I loop through these clusters and step increment each cluster by 20 (10 2's), the second cluster will have 10 equal values of 120 each, the third cluster will have 10 equal values of 140 each.. and so on.
'
'To this cluster, I need to add the cluster of 2's. I need to calculate this cluster only once and add it to each one of the "denominator-clusters" and then add all the clusters together which gives me the final total sum.
'
'To add the cluster of 2's, I could hard-code that:
'2+4+6+8...+20=110
'But once again, if the intent of the puzzle is to be able to substitute for other values, I will use a loop to add these incrementing 2's, which means I will loop 10 times to calculate the cluster of 2's then loop another 10 times to calculate the "denominator-clusters" and in each loop I am adding each one of the to the previous total plus the sum of the cluster of 2's so at the end of the last loop. After that I will find the orphan values, the ones that were not included in the clusters and add those to the total which gives me the grand total.
'Now why did I choose 10 clusters?
'That produces the "optimal" number of loops in this scenario:
'If you increase the size of the cluster to reduce their number and thus the number of looping through them, you will increase the number of 2's and the number of their loops.
'How to arrive at the optimal cluster size?
'That's for another day another post, but regardless, any number of clusters will beat the standard looping method.```
Here is the script:
Code:
```'For further explanations, please read the Introduction section
option strict
dim bottom_num as n
dim top_num as n
dim denominator as n
dim span as n 'the span between the bottom and top numbers
dim values_num as n
dim i as n 'to be used as a counter
dim twos as n'this will add the 2's that are above and beyond the denominator values
dim vtotal as n=0
dim trail_num as n'number of orphan values not in the clusters
dim trail_values as n'the actual value of the orphan
dim loop_num as n'how many times we looped so far
dim last_even as n'this is the value of top-most even number in the series
bottom_num=101
top_num=302
span=top_num-bottom_num
values_num=int(span/2)+1 'This is how many even number in the span between the bottom and top numbers. The 1 is added to make it all inclusive, i.e. including the bottom as well as the top numbers
trail_num=mod(values_num,10)
denominator=bottom_num-if(mod(bottom_num,2)=0,0,1)
for i=1 to 10
twos=twos+i*2
next i
loop_num=i
'Now we will iterate over the "denominator-clusterss" , each cluster will have a denomiator value of 20 more the one before
for i=1 to 10
vtotal=vtotal+(denominator+20*(i-1))*10+twos
next i
loop_num=loop_num+i
'Now we will add the trailing numbers, those that were not included in the 10 clusters
'Find the last even number:
last_even=if(mod(top_num,2)=0,top_num,top_num-1)
for i= 1 to trail_num step-1
trail_values=trail_values+last_even
last_even=last_even-2
next
loop_num=loop_num+1
vtotal=vtotal+trail_values
msgbox("The sum total of all even numbers is: "+vtotal+" "+"and the number of loops is: "+loop_num)``` #### Posting Permissions

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