# Cryptarithmetic Problem-2

Multiplication

A | B | C | |||

D | E | C | |||

F | G | H | |||

I | A | C | |||

A | C | A | E | ||

A | F | A | G | C | H |

Solution:

**First if you see ( D E C ) * C from this we can confirm that two possibilities:**

**1) E = ( 3, 7, 9 ) and C = 5**

**2) E = 6 and C = ( 2, 4, 8 )**

**So now you are in little bit confusion which possibility I should proceed.**

**If you are not choosing the correct possibility time will be killed off course time is very very precious in eLitmus exam.**

**So, better step forward to estimate the correct possibility–)**

**If you see last multiple ( D E C ) * C = E if you assume C = 5 and E = (3, 7, 9 ) the only possible values ofD = (2, 4, 8) if you keep any value for D then the value E = 0 that is contradiction.**

**So it is very clear that first possibilities is wrong then go with the second possibility means**

**E = 6 and C = (2, 4, 8) Let’s take C = 2 Then the table changes as:**

A | B | 2 | |||

D | 6 | 2 | |||

3 | 0 | 4 | |||

I | A | 2 | |||

A | 2 | A | 6 | ||

A | 3 | A | 0 | 2 | 4 |

**Clearly from the table H = 4 and G = 0 (because G + 2 = 2 means G = 0), and F = 3 (C + carry= F).**

**After filling this values let’s take (A B 2) * 2 = 3 0 4. It happens only when B = 5 and A = 1**

**Replace the values and redraw the table.**

1 | 5 | 2 | |||

D | 6 | 2 | |||

3 | 0 | 4 | |||

I | 1 | 2 | |||

1 | 2 | 1 | 6 | ||

1 | 3 | 1 | 0 | 2 | 4 |

**From the table (1 5 2) * D = 1 2 1 6 It will happen only when D = 8 and from the line (I + 1 + carry = 1) so from that we can say I = 9.**

**Replace all the values,**

1 | 5 | 2 | |||

8 | 6 | 2 | |||

3 | 0 | 4 | |||

9 | 1 | 2 | |||

1 | 2 | 1 | 6 | ||

1 | 3 | 1 | 0 | 2 | 4 |

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i cant undrstd plz explain

ReplyDeleteWhich Step..?...pls mention the part i which u faced problems

DeleteHow do we know that carry is 1 in case of c+carry=f?

DeleteFinal result should be 431024 that means HFAGCH, not AFAGCH

ReplyDeleteMULA please check your answer...!!! It is 131024

ReplyDeleteHow do we know that carry is 1 in case of c+carry=f?

DeleteHow do we know that carry is 1 in case of c+carry=f?

ReplyDelete