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Numbers Puzzle

Find all solutions to \( \sqrt{PASSION} = MISS \) where alphabets stand for distinct digits from 0 to 9.

I 've got an answer by reducing thousands of possibilities to some fifty to hundred and then trial n error. Looking for precise logical arguments leading to solution. Plz help.

Note by Piyushkumar Palan
3 years, 5 months ago

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Finally got it.

A long sequence of logical mathematical arguments n Possibilities of MISS reduced to just 6. Then squared all six and only one matches with form of PASSION.

MISS = 2033 is the only solution. Piyushkumar Palan · 3 years, 5 months ago

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EDIT

I am sorry About Previous Post,I got the following pairs upon revision

0000 0000000
1000 1000000
2000 4000000
3000 9000000
2033 4133089
1312 1721344

The following prints all possible \(MISS,PASSION\) pairs

print 'MISS','PASSION'
Squares = set([i**2 for i in range(10**5)])
for miss in range(0,10000):
    MISS = str(miss)
    if miss < 1000:
        MISS = '0'*(4-len(MISS))+MISS
    PASSION = str(miss**2)
    if len(PASSION)>7:continue
    else:PASSION = '0'*(7-len(PASSION))+PASSION
    if PASSION[2:5] == MISS[1:][::-1] and len(PASSION)==7:
            print MISS,PASSION
Thaddeus Abiy · 3 years, 5 months ago

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@Thaddeus Abiy hey thanks for ur attempt. But there is/are non-trivial solution(s), where each alphabet stands for different digit. Piyushkumar Palan · 3 years, 5 months ago

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@Piyushkumar Palan Sorry,Look at my re-edited solution above Thaddeus Abiy · 3 years, 5 months ago

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@Thaddeus Abiy yes MISS = 2033 is the only correct solution. Piyushkumar Palan · 3 years, 5 months ago

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@Piyushkumar Palan hi piyush, i did the same way. but had to use machine (spreadsheet) for shortlisting 6 possibilities. without machine, i could reach up to m=1,2,3 and s=2,3,4,7,9. please let me know if u found the answer without using machine (calculator or computer). Abhijit Gokhale · 2 years, 7 months ago

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