# 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
4 years, 4 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.

- 4 years, 4 months ago

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


- 4 years, 4 months ago

hey thanks for ur attempt. But there is/are non-trivial solution(s), where each alphabet stands for different digit.

- 4 years, 4 months ago

Sorry,Look at my re-edited solution above

- 4 years, 4 months ago

yes MISS = 2033 is the only correct solution.

- 4 years, 4 months ago

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).

- 3 years, 6 months ago