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HeaRT OF VENUS (Posted on 2011-09-18) Difficulty: 3 of 5
Solve the following alphametic, given that two are primes and one is a composite:

SEVEN - THREE = FOUR

BONUS: Without the restriction of the number of composites and primes in the alphametic, how many different solutions are there?

See The Solution Submitted by Dej Mar    
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Some Thoughts PARTIAL SOLUTION | Comment 2 of 3 |

 FOUR+THREE=SEVEN

From this list(alphametic solver):

2503+69311=71814

9503+62311=71814

2904+68411=71315

8904+62411=71315

2906+38611=41517

 

8906+32611=41517

5207+36711=41918

6207+35711=41918

3408+57811=61219

7408+53811=61219

 

4708+26811=31519

6708+24811=31519

3104+79422=82526

9104+73422=82526

3106+49622=52728

 

9106+43622=52728

3407+58722=62129

8407+53722=62129

4902+68233=73135

8902+64233=73135

 

6405+17533=23938

7405+16533=23938

5806+17633=23439

7806+15633=23439

5102+79244=84346

 

9102+75244=84346

6805+17544=24349

7805+16544=24349

6902+38255=45157

8902+36255=45157

 

6403+19355=25758

9403+16355=25758

6704+28455=35159

8704+26455=35159

7495+28566=36061

 

8495+27566=36061

7102+49266=56368

9102+47266=56368

 

 

 

we erase the raws with more than one even number or even number and mult. of 5:

2503+69311=71814

9503+62311=71814

2904+68411=71315   erased

8904+62411=71315erased

2906+38611=41517

 

8906+32611=41517

5207+36711=41918

6207+35711=41918

3408+57811=61219

7408+53811=61219

 

4708+26811=31519

6708+24811=31519

3104+79422=82526erased

9104+73422=82526erased

3106+49622=52728erased

 

9106+43622=52728erased

3407+58722=62129

8407+53722=62129

4902+68233=73135erased

8902+64233=73135erased

 

6405+17533=23938erased

7405+16533=23938erased

5806+17633=23439

7806+15633=23439

5102+79244=84346erased

 

9102+75244=84346erased

6805+17544=24349erased

7805+16544=24349erased

6902+38255=45157erased

8902+36255=45157erased

 

6403+19355=25758erased

9403+16355=25758erased

6704+28455=35159erased

8704+26455=35159erased

7495+28566=36061erased

 

8495+27566=36061erased

7102+49266=56368erased

9102+47266=56368erased

 

we are left with:

2503+69311=71814

9503+62311=71814
2906+38611=41517

8906+32611=41517

5207+36711=41918

6207+35711=41918

3408+57811=61219

7408+53811=61219

4708+26811=31519

6708+24811=31519

3407+58722=62129

8407+53722=62129

5806+17633=23439

7806+15633=23439

 

Too lazy to check for composite/prime - leave it to oyhers.

 

 

 

 

 

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  Posted by Ady TZIDON on 2011-09-18 14:43:06
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