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Cryptarithmetic Problem-1

Ayush Agarwal | 07:43 | 15 comments

Multiplication

PROB 2
WHY
NUT
OONP
OYPY
OUHA
ONEPOP


When you see second multiple (W H Y ) * U = (O Y P Y)
So, The number for U = 6 and Y is (2 , 4) Lets take the value of Y is 4 and replace it in figure.


WH4
N6T
OONP
O4P4
O6HA
ONEPOP

Clearly if you see the yellow portion O + 6 = N and there is no carry to the next digit so we can confirm that ‘N’ is single digit number. If ‘N’ is single digit number ‘O’ should be less than (O < 3)
Let’s take O = 1 and redraw the table…

WH4
N6T
11NP
14P4
16HA
1NEP1P
If you observe 1 + 6 = N & N + 4 = 1 so, we can clearly the value of N =7
So replace N = 7 and redraw the table.
WH4
76T
117P
14P4
16HA
17EP1P

Take the third multiple (W H 4) * 7 = 1 6 H A    from this we get A = 8, and if you replace the H with 3 and w = 2 then the equation satisfies.
Like (2 3 4) * 7 = 1 6 3 8 so redraw the table with particular values.

234
76T
117P
14P4
1638
17EP1P


The remaining numbers are (0,5,9) It is simple to analyse we can’t get 5 in place of p because when you multiply with 4 we cannot get the last digit as 5.
So T = 5, P = 0, E = 9
After redraw the table.

234
765
1170
1404
1638
17901
0

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15 comments:

  1. In first step we can also take U=3 & Y=5 .So there are many possibilities how can you guess the right one..

    ReplyDelete
  2. First of all Y never be 5 (cause 5* odd= 5 and 5*even= 0.So if Y=5 then Y*odd=Y and Y*even=0 so only two letter with signify 0 and 5 where as Y=5 then ) will be some other letter.Now Y*T=P and Y*N=A, so either P=0 or A=0 but both together can't be 0.So Y= 5 never be possible.)
    Now U = 6 because 6*even = that number. So 6*Y=Y (Here Y maybe 2 or 4)

    If any further problems are there pls comment here.

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    1. This comment has been removed by the author.

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    3. U=6 s clear. How you approached for Y=2/4? Why not 8?

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    4. Nice approach.
      But how to reach decision for Y as 2 or 4 only, but not as 8?

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    5. how did u take y as 2 n 4 not 6 and 8?

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  3. Think in proper way.before starting direct problems just think what will be the possibilies and combinations.

    ReplyDelete
  4. why it cant be 6 and 8 => 8*6=48 and

    ReplyDelete
  5. @admin
    ur approach is good i have one small doubt
    in 1st step you said U=6 and Y=(2,4) but,here Y can take 8 also
    what makes you think to leave that possibility(y=8)?

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  6. This comment has been removed by the author.

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  7. in the beginning how did u take u as 6 and y as 2 or 4

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  8. Hello i am completley new to these kind of problems can u help me in understanding from basics

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  9. Hello i am completley new to these kind of problems can u help me in understanding from basics

    ReplyDelete