The missing numbers

Computer Science Level 3

This text file contains a list of arithmetic progression with a common difference of 4 4 . At random three numbers were removed from the list excluding the beginning and end. If ( A 1 , A 2 , A 3 ) (A_{1},A_{2},A_{3}) are the three such numbers in increasing order..

A 3 − ( A 2 + A 1 ) = ? A_{3}-(A_{2}+A_{1})= ?


The answer is 7589.

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Beakal Tiliksew by Beakal Tiliksew , 24, Ethiopia

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2 solutions

Bill Bell
Sep 6, 2015 
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terms=[3, 7, 11, ... ]

missings=[]
for i in range(-1+len(terms)):
    if terms[i+1]-terms[i]==8:
        missings.append((terms[i+1]+terms[i])/2)
A1, A2, A3=missings
print A3-(A2+A1)

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice, short code. It is possible that the terms that were removed from the sequence were consecutive, so we should also check for cases where the difference terms[i+i] - terms[i] is 12 and 16.

Pranshu Gaba - 5 years, 9 months ago

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You are quite right. I was lucky. Come to think of it, that would have made a much better problem, if the three numbers had been deliberately selected so that what you suggested could have been made to happen.

Bill Bell - 5 years, 9 months ago

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i could have done that, but that wouldn't have made it harder only more error prone. I mostly focused on a generalized binary search to solve this problem

Beakal Tiliksew - 5 years, 9 months ago

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@Beakal Tiliksew – I'm disinclined to argue very long about this but making people (like me) look for leaks in code is generally a good thing.

I am sorry to have given offence. I think I've contributed all of two problems myself. ;)

Bill Bell - 5 years, 9 months ago

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@Bill Bell – i see no offense in your remarks, i fully agree with you in finding leaks in a code, which is why i think it would be preferable if the questions provided test cases.

Beakal Tiliksew - 5 years, 9 months ago

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@Beakal Tiliksew – Naw! Let us all trip over our own feet.

Bill Bell - 5 years, 9 months ago
Aareyan Manzoor
Sep 19, 2015

very quick code and short code python:

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Could be shorter: 

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leftovers = [x for x in list(range(min(ap), max(ap) + 4, 4)) if not x in ap]

Abdelhamid Saadi - 5 years, 8 months ago

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