Cryptarithmetic Problems

Cryptarithmetic Pr Problems

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Cryptarithmetic Problems

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Cryptarithmetic Cryptar ithmetic Problems; Everyone's favorit favorite e mathematical puzzle puzzle Topic Started: 24 Jul 2009, 06:36 AM (29,668 Views)

VirtualSerendipity

24 Jul 2009, 06:36 AM

Post #1

What is a cryptarithmetic problem? problem? It is a mathem mathematical atical puzzle in which each l etter represents a digit (for example, if X=3, then XX=33). XX=33). The object is to find the val ue of each letter. No two letters represent the same digit (If X=3, X=3, Y cannot be 3). And the first letter cannot be 0 (Given the value ZW, Z cannot be 0). T hey can be quite chall enging, often involving many steps. Established Member

Here's an example, illustrating how to solve them:

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Member #55 Joined: July 10, 2009

MONEY

M must be 1. If you'll notice, this is an addition problem; the sum of two four digit numbers can't be more than 10,000, and M can't be 0 according to the rules since it's the first letter. So now



Cryptarithmetic Problems; Everyone's favorite mathematical puzzle you have:

. SEND +1ORE 1ONEY

Now in the column S1O, S+1 ≥10. S must be 8 (if there is a 1 carried over from the column E0N) or 9. O must be 0 (if S=8 and there is a 1 carried or S=9 and there is no 1 carried) or 1 (if S=9 and there is a 1 carried). But 1 i s already taken, so O must be 0.

. SEND +10RE 10NEY

There can't be a carry from the column E0N, because any digit pl us 0 < 10, unless there is a carry from the column NRE and E=9; but this cannot be the case, because then N would be 0, and 0 is already taken. S o E<9 and there i s no carry from this column. Therefore, S=9, because 9+1=10.

. 9END +10RE 10NEY

In the column E0N, E cannot be equal to N, so there must be a carry from the column NRE; E+1=N. We now look at the column NRE; we know that E+1=N. Since we know that there is a carry from this column, N+R=1E (if there is no carry from the column DEY) or N+R+1=1E (if there is a carry from the column DEY). Let's try out both cases.

No carry: N+R=10+(N-1)=N+9 R=9 9 is already taken, so this won't work.

Carry: N+R+1=N+9 R=8 This must be the solution for R.

. 9END +108E 10NEY

The digits we have left are 7, 6, 5, 4, 3, and 2. We know there must be a carry from the column DEY, so D+E>10. N=E+ 1, so E can't be 7 because then N would be 8 which is already taken. D is at most 7, so E cannot be 2 because then D+E<10, and E cannot be 3 because then D+E=10 and Y=0, but 0 is taken already. Likewise, E cannot be 4 because if D>6, D+E<10, and if D=6 or D=7, then Y=0 or Y=1, which are both taken. So E is 5 or 6.

If E=6, then D=7 and Y=3, so this part works. But look at the column N8E. Remember, there is a carry from the column D5Y. N+8+1=16 (because we know there is a carry for this column). But then N=7, and 7 is taken by D. Therefore, E=5.

. 95ND +1085



Cryptarithmetic Problems; Everyone's favorite mathematical puzzle 10N5Y

Now that we've gotten this important digit, it gets much simpler from here. N+8+1=15, N=6.

. 956D +1085 1065Y

The digits left are 7, 4, 3, and 2. We know there is a carry from the column D5Y, so the only pair that fits is D=7 and Y=2

. 9567 +1085 10652

And Voila! T he problem is solved! T hese are quite tricky and require some thinking, but are lots of fun. Now we'll take turns posting problems. When a problem is solved, you may post another problem. Be sure to show your work; you don't have to write detailed instructions like I did, but show your steps at least, si nce figuring out how to solve the problem is the most important part. I'll start things off here:

. . EAT +THAT APPLE

uberking

24 Jul 2009, 08:53 PM

Post #2

. . EAT +THAT APPLE

I started off knowing that T is not 0, as T+T is not equal to T. Same case with A. From know on, I'm gonna show the steps to my answer. Don't ask HOW I got them, it's too much work that I did on a piece of paper. And I can't type all that. Posts:

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. . EA9 +9HA9 APPLE

. . 8A9 +9HA9 APPL8



Cryptarithmetic Problems; Everyone's favorite mathematical puzzle . . 819 +9H19 APPL8

. . 819 +9H19 APP38

. . 819 +9219 A0038

. . 819 +9219 10038

FINAL ANSWER:

. . EAT . . 819 +THAT +9219 APPLE 10038

--made by download 'cuz I has no pro GIMP skills

VirtualSerendipity

25 Jul 2009, 03:34 AM

Feel free to post a new problem when you solve one. Here's another problem:

. TAKE ....A +CAKE Established Member

. KATE

Post #3



Cryptarithmetic Problems; Everyone's favorite mathematical puzzle

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download

29 Nov 2009, 06:47 AM

Post #4

3961+9+2961=6931

I have to admit i cheated. T here's quite a few programs out there that solve cryptarithmetic problems. I wonder how they do it... Founder

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By the way, here's another problem.

BASE+BALL=GAMES Edited by download , 30 Nov 2009, 04:49 AM.

-download | the administration

Add this to your signature

chezemaster

7 Dec 2009, 02:31 AM

I can't solve that problem Cheesy Responses requires response from the Cheesy Master of Doom

NO + NO = YES That, by the way, was my Educated Guess

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Don't try to be wi tty and write sarcasti c things when you write things. If you want to be sarcastic at least do this: ***insert sarcasm here***

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just trying to be useful

Inkscape is e qual to or larger than GIMP

Post #5




download

7 Dec 2009, 02:39 AM

Post #6

There's a lot of possibilities to your problem:

79+79=158 69+69=138 78+78=156 Founder

67+67=134 86+86=172

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76+76=152 85+85=170 65+65=130 64+64=128 54+54=108 93+93=186 73+73=146 53+53=106 92+92=184 82+82=164 52+52=104



markomitr

10 Apr 2010, 11:34 AM

Post #7

Please help me

TWO + THREE = FIVE ????

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download

10 Apr 2010, 11:29 PM

markomitr

Post #8

10 Apr 2010, 11:34 AM



Cryptarithmetic Problems; Everyone's favorite mathematical puzzle Founder

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Please help me

TWO + THREE = FIVE ????


Your problem isn't possible, as "THREE" has five characters, while the sum, "FIVE," only has four.



ashish

28 Oct 2010, 01:49 PM

Post #9

cross+roads=danger cross+roads=danger ashish New Member

28 Oct 2010, 01:49 PM

cross+roads=danger cross+roads=danger

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Edited by ashish , 28 Oct 2010, 01:55 PM.

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anal

15 Dec 2010, 01:38 PM

Post #10

Link 4 all the solution ::: http://bach.istc.kobe-u.ac.jp/cgi-bin/crypt/crypt.cgi?crypt=no%2Bno%3Dyes

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Red Daisuke

2 Jan 2011, 01:32 PM

Post #11




anal

15 Dec 2010, 01:38 PM

Link 4 all the solution ::: http://bach.istc.kobe-u.ac.jp/cgi-bin/crypt/crypt.cgi?crypt=no%2Bno%3Dyes The Green Arrow

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That pretty much takes the fun out of it.

Member #74 Joined: September 17, 2009

Amethyst

20 Oct 2011, 03:11 AM

Post #12

This is very cool stuff....unfortunately I'm not sure how to solve these.

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Jak Atackka

21 Oct 2011, 03:49 PM

I've got one - CARBON + DIOXIDE = WARMING I've got one - CARBON + DIOXIDE = WARMING Try solving without the tool. Wise Guy Edited by Jak Atackka , 21 Oct 2011, 03:49 PM. Posts:

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Post #13




download

21 Oct 2011, 03:52 PM

Post #14

21 Oct 2011, 03:49 PM

Jak Atackka I've got one - CARBON + DIOXIDE = WARMING I've got one - CARBON + DIOXIDE = WARMING Try solving without the tool.

Founder

Very interesting problem - one question first, is there only ONE solution? Seems like there are

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too many variables for there to be one solution; then again, if all the letters represent a different number that'd work.




Jak Atackka

21 Oct 2011, 04:20 PM

Post #15

By each variable representing a different number, do you mean that, for example, the two Ds in DIOXIDE are two different digits? If so, no. Also, since there are 13 different variables, some variables might have the same value. Wise Guy

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