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Alphametics- The Art of Numbers
by Total Gadha - Friday, 15 February 2008, 03:27 PM
 

cat 2008 xat 2008 mba 2008 cat 2009 alphameticsAs CAT 2008 preparation starts heating up, I am going to flag the race with an oddball topic: Alphametics. What are alphametics or cryptarithms as they are also known? Alphametics are number puzzles in basic arithmetic operations where digits are represented by alphabets. It is customary that different digits are represented by different alphabets. Why are alphametics relevant? Because they require a good knowledge of properties of numbers and skill in working with them. Solving alphametics helps you quickly identify solution to many problems which might otherwise require a good amount of time. Let me give an example:



Can you solve this problem without any hit or trial method?



alphametics cat 2008 cat 2009 xat 2008


cat 2008 alphametics

I am afraid I shall have to end here and leave the rest of it for my CBT Club students. I shall cover some problems based on this in the CBT Club this week.

 

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Re: Alphametics- The Art of Numbers
by Anshuman Bhar - Friday, 15 February 2008, 05:56 PM
  Hi Tg,
 These days I am busy solving ur number system problems...jss now I saw this article..man u rock.... I mst say very very useful dedicated website is this for CAT.....I hope I get through CAT this time...thanks a lotzz TG
Re: Alphametics- The Art of Numbers
by Total Gadha - Friday, 15 February 2008, 09:31 PM
  Thanks Anshuman smile
Re: Alphametics- The Art of Numbers
by jai prakash - Friday, 15 February 2008, 11:00 PM
  THANKS A GOOGLE OF TON FOR THIS ENLIGHTMENT.
If i make it to a top MBA institute 80% of the credit goes to
ur support n inspiration.
EXPECT MORE 4M U.
Re: Alphametics- The Art of Numbers
by PRIYANKA KESHRI - Saturday, 16 February 2008, 03:10 PM
 

hi!!!!!!

tg .. joined ur forum a few days ago... ur a ultimate genius man... superb article... just keep the good work on and we will surely bell the cat this time... thanx a million  for ur superb masterpiece

Re: Alphametics- The Art of Numbers
by PRIYANKA KESHRI - Saturday, 16 February 2008, 06:11 PM
 

hi!!

just tried out ur posted problems.. got my ans as

1)1089*9=9801

2)25*25=625

3)????

hey dont know wats the r8 one... kindly post the ans wid ur mindblowing solns.. and any clues 4 the 3rd one.. i am not getting it..

Re: Alphametics- The Art of Numbers
by Total Gadha - Saturday, 16 February 2008, 08:51 PM
  Hi Priyanka,

Well done. smile

Will post the solution to the third one after others have also tried. smile

Total Gadha
Re: Alphametics- The Art of Numbers
by santaneel pyne - Saturday, 16 February 2008, 10:13 PM
  76211 + 76211 + 8592 = 161014


Re: Alphametics- The Art of Numbers
by gOd's chILd!! - Sunday, 17 February 2008, 01:04 AM
 

gud morning sir;

78011+78011+5390=161412

pls let me know if i'm wrong..!

Re: Alphametics- The Art of Numbers
by gOd's chILd!! - Sunday, 17 February 2008, 01:17 AM
 

santaneel i think we need to assign different values to H and l

tHree=76211(H=6)

+ tHree=76211(H=6)

+ four=8592

=eLeven=161014(L=6)

 

Re: Alphametics- The Art of Numbers
by PRIYANKA KESHRI - Sunday, 17 February 2008, 01:41 AM
  thanx TG sir u have boosted up my morale!!!!!!!!!!!!
Re: Alphametics- The Art of Numbers
by bimal mohan - Sunday, 17 February 2008, 09:20 AM
 

Third one:

84011 +84011+3590 =171612

Re: Alphametics- The Art of Numbers
by santaneel pyne - Sunday, 17 February 2008, 05:51 PM
  yah! ur right, i got it wrongapprove
Re: Alphametics- The Art of Numbers
by Total Gadha - Sunday, 17 February 2008, 07:30 PM
  smile smile
Re: Alphametics- The Art of Numbers
by Prateek Agarwal - Tuesday, 19 February 2008, 07:56 PM
  Thanks TG...that was really helpful
Re: Alphametics- The Art of Numbers
by Harpreet Singh - Monday, 25 February 2008, 10:55 PM
 

Hi,

Do the third question has multiple solutions. Well thanks for such a gr8 exercise.

Rgards,

Harpreet

 

Re: Alphametics- The Art of Numbers
by Avishek Chakravarti - Thursday, 28 February 2008, 11:24 PM
 

Yes

83211+83211+4592=171014

ANOTHER SOLUTION

Re: Alphametics- The A
by avinash gupta - Friday, 29 February 2008, 01:23 PM
  hey that was a great insight into numbers...but thers a small glitch..when u eliminated numbers(TWO*TWO=THREE)11,55,99 ur argument was that the tens digit of the square in never odd except for 6...but there's a possilblty of a carry over resulting in a odd number right?? the method u suggested was impressive on the surface ....i alwasy find it difficult to fathom out when it comes to such kind of problems..
Re: Alphametics- The A
by Total Gadha - Friday, 29 February 2008, 04:50 PM
  hi Avinash,

I repeat, "the tens digit of a perfect square is always even except when the unit digit is 6 in which case the tens digit is odd." Carry or no carry. Try it out. smile

Total Gadha
Re: Alphametics- The Art of Numbers
by Naveen Naveen - Wednesday, 5 March 2008, 12:48 PM
 

Hi TG,

Thanks for your efforts, i have just started on this site...i mean replying...

I am solving the problem you are posting...but can you tell me where do u post the solution...do you post them on this thread it self or is there is any other thread for posting solutions?

Thanks

Re: Alphametics- The Art of Numbers
by Prashant Chanchal - Wednesday, 5 March 2008, 01:17 PM
  Hi The third one seems to have more than 3 (May Be 100s!) of possible solutions! I came up with: 78011 +78011 + 5390 ------- 161412 ------- Would request TG to post the solution (few) with proper logic as in how to go about this one!
Re: Alphametics- The Art of Numbers
by Sreedevi PV - Thursday, 6 March 2008, 12:58 PM
 

Hello TG,

The article rocks. got to know lot of small things ......

Thanks a lot....

Re: Alphametics- The Art of Numbers
by Jaidev Nair - Tuesday, 11 March 2008, 03:07 PM
  Hey please tell me what was your appraoch like....its taking too long to solve
Re: Alphametics- The Art of Numbers
by Jaidev Nair - Tuesday, 11 March 2008, 03:08 PM
  Hey please tell me what was your appraoch like....its taking too long to solve
Re: Alphametics- The Art of Numbers
by manish jain - Monday, 17 March 2008, 07:16 PM
  hi
Re: Alphametics- The Art of Numbers
by ganesh ram - Sunday, 10 August 2008, 10:58 PM
 

HATS OF TO UOU TG................

WHAT A ARTICLE IT IS.............

Re: Alphametics- The Art of Numbers
by MBA CrAcker - Thursday, 14 August 2008, 09:58 AM
  Please write the solution of the third Question(THREE + THREE + FOUR = ELEVEN), My approach seems to be a bit longer
Re: Alphametics- The Art of Numbers
by rick patel - Saturday, 16 August 2008, 04:12 AM
  I don't want 2 say this but u really r TOTAL GADHA.....awesome post n awesome methods....
U simply rock man...
Re: Alphametics- The Art of Numbers
by Vaibhav Gayake - Tuesday, 19 August 2008, 02:00 PM
 

Please post the answer for the third question.(Stepwise Approch)

 

Regards,

 

Vaibhav

 

Re: Alphametics- The Art of Numbers
by ajay singh - Wednesday, 20 August 2008, 10:35 AM
 

Very good site .

Ajay Singh

Mumbai

Re: Alphametics- The Art of Numbers
by preeti jha - Thursday, 21 August 2008, 12:28 PM
 

Hi TG,

Nice approach...You are doing a grt job!! Please provide some more sums...and also the solution to last one.

Regards,

Preeti

Re: Alphametics- The Art of Numbers
by ankit mahajan - Friday, 22 August 2008, 02:10 PM
 

can somebody explain the below CAT 2001 question

Q.25 Ram has 128 boxes with him. He has to put atleast 120 oranges in one box and 144 at the most. Find the least number of boxes which will have the same number of oranges.

1) 5 2) 6 3) 103 4) Can’t determine.

(read somewhere that it involves pigeon hole principle)

TG can you be kind enough to explain the ques and Pigeon Hole funda and how it applies here..

Re: Alphametics- The Art of Numbers
by deepa awasthi - Friday, 22 August 2008, 08:28 PM
  Hey I must say..quite a useful article ..thanks a ton for helping us all MBA aspirants smile 
Re: Alphametics- The Art of Numbers
by Aashish Dua - Friday, 29 August 2008, 01:14 AM
 

Hie TG Sir,

An awesome article once again.

Thanks Sir

Re: Alphametics- The Art of Numbers
by neha prasad - Saturday, 6 September 2008, 09:04 PM
  Superb article .....Thanks a lotsmile
Re: Alphametics- The Art of Numbers
by ravi mr. - Thursday, 16 October 2008, 05:13 PM
  ABCD x 9 = DCBA Sol: 1 0 8 9 X 9 9 8 0 1 AH X AH = BAH Sol : 2 5 x 2 5 6 2 5 T H R E E T H R E E + F O U R E L E V E N SOL: 5 7 2 1 1 5 7 2 1 1 + 6 8 9 2 1 2 1 3 1 4
Re: Alphametics- The Art of Numbers
by ravi mr. - Thursday, 16 October 2008, 05:23 PM
  ABCD x 9 = DCBA Sol: 1 0 8 9 X 9 = 9 8 0 1 AH X AH = BAH Sol : 2 5 x 2 5 = 6 2 5 T H R E E + T H R E E + F O U R = E L E V E N SOL: 5 7 2 1 1 + 5 7 2 1 1 + 6 8 9 2 = 1 2 1 3 1 4
Re: Alphametics- The Art of Numbers
by Rajakannan R - Sunday, 15 March 2009, 06:28 PM
 

Hi Tg sir,

Soln for 3rd question

74611 + 74611 + 2096 = 151318..Is it correct?

Is there any good approach to solve this prob? I did it by trail n error..

Re: Alphametics- The Art of Numbers
by prachi joshi - Friday, 20 March 2009, 04:02 PM
  sir
can u pls explain the third one
Re: Alphametics- The Art of Numbers
by Pranav Baj - Monday, 30 March 2009, 02:16 PM
  great job man thnx for enlightenin
Re: Alphametics- The Art of Numbers
by krd sh - Saturday, 3 October 2009, 05:40 PM
 

ABCD * 9 = DCBA = 1089*9 = 9801

AH * AH = BAH= 25 * 25 =625. How? We have to find a perfect square that result in last two digits being the same as the numbers AH. There are only three numbers. 1*1=1, 5*5 = 25 and 6*6= 36 out of which only 5*5 only satisfies the solution.

THREE + THREE + FOUR = ELEVEN

78011+ 78011+ 5390= 161412

ABCD * 4= DCBA = 2178* 4= 8712

Re: Alphametics- The Art of Numbers
by Pallav Jain - Saturday, 3 October 2009, 07:28 PM
 

hI tG,

hATS oFF

Re: Alphametics- The Art of Numbers
by Deepak Gautam - Monday, 5 October 2009, 04:19 AM
  Hi, T.G
Thanks for the good questions,
Credit should also go to "Software Engineer" too.
See the "God of small things" thread in Quant forum.
that's what we call congregation of thoughts and Ideas pouring from different sides and shades. hats off to ur efforts T.G.
Thanks
Deepak Gautam(A.k.a Chill Pill)
Re: Alphametics- The Art of Numbers
by Deepak Gautam - Monday, 5 October 2009, 04:15 PM
 
Correction:the thread was
Skeleton in the Problem Solving Closet
by quant ghost.
Re: Alphametics- The Art of Numbers
by The Game - Wednesday, 11 November 2009, 05:14 PM
 

1) 1089*9=9081

2)25*25=625

3)

Re: Alphametics- The Art of Numbers
by Ajay Sharma - Wednesday, 11 November 2009, 11:48 PM
  Hi Sir,

Can u pls provide the solution for 3rd one(Stepwise)

I m not able to get the lead after getting E=1 and U=9
Re: Alphametics- The Art of Numbers
by vikas khanna - Tuesday, 17 November 2009, 11:54 AM
  plz look it on this question..
Re: Alphametics- The Art of Numbers
by amar goswami - Wednesday, 18 November 2009, 12:08 AM
  pi + psi + gamma =  sigma
each alphabet rapresent a digit between 0-9.getting i as 0 or 5.
i got no other way but hi and trial...
sir plz help me out...
if there is any mathematical approach to solve this problem..


Hi Vikas,

   Please find the solution to ur problem below:
    pi
   psi
+gamma
------
 sigma
------
70 + 730 + 29449 = 30249
i.e.

    70
   730
+29449
------
 30249
------

it can be infered from question that maximum carry which can go from i to g is 1 hence g + 1 = s   ------- (i)
again since p + m <20 always hence maximum carry which can go from g to a is 1 i.e. a + 1 = i  which implies a =9 and i=0 because  9+1 = 10,
hence we get i =0. Now it is clear that unit digit of sum of p+s+m comes as m hence p+s+m = 10 + m   (only possibility) --------- (ii)
also p + m = 10 +g   (since it has to pass one carry to a) ------ (iii)
from above three equations we get
m=2g   and   m =2s - 2
g can take value from 1 to 4 and g =2 gives the result.

Thanks
Amar

Re: Alphametics- The Art of Numbers
by vikas khanna - Wednesday, 18 November 2009, 06:17 PM
  thanx amar...this is really good.
vikas.
Re: Alphametics- The Art of Numbers
by kunal kaira - Friday, 20 November 2009, 05:39 PM
  ...
Re: Alphametics- The Art of Numbers
by surabhi gupta - Monday, 30 November 2009, 12:32 AM
  Can smone tell the solution of the third problem???
Re: Alphametics- The Art of Numbers
by New Donky don - Monday, 30 November 2009, 01:25 PM
  @ surbhi
see here it goes.....

ab*cb=ddd
dis is a common method or say concept that  is case of 3 digit no. xxx factorization is done only by 37*3  or 3x*111 
37 is a 2 digit no. but 3 is not so we need to convrt 3 into a 2 digit no. and it shud be a multiple of 3 u can chk it out
37*3 = 111
37*6 = 222
37*9 = 333
so 3,6,9,12,15,18,21,24,27
so 37*27 = 999

hope its clear now

beers!!!
new donky
Re: Alphametics- The Art of Numbers
by gaurav midha - Thursday, 9 February 2012, 08:40 AM
  Hi TG/Kamal Sir,

I have a doubt in the above question in which ABC x CBA = 65125 where A, B and C are single digits , then A+B+C=?

How we reach on the conclusion :- "product would give sum of a perfect square.The digit sum on RHS is 1.Therefore, the digit sum of each number can be 1, 8 or 10.Correspondingly B will be 2 or 4(as digit sum cannot be equal to 1)."

Please throw some more light on it.

Thanks.
Re: Alphametics- The Art of Numbers
by gaurav midha - Friday, 10 February 2012, 09:18 AM
  Hi TG/Kamal Sir,

I have read the article on Digit Sum of numbers.

Thank you.