One time in college I emailed my dad asking for money and he said I could have some if I solved the following equation:

SEND

+MORE

_______

MONEY

Each letter represents its own digit (0-9) and multiple occurrences of the same letter represent the same digit (eg if one of the E's represents a 3, they all do).

Solution:

9567

+ 1085

-----------

10652

## Wednesday, August 18, 2010

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After several hours of vigorous problem solving and guess-and-check, I think I've come upon the solution.

ReplyDelete9567

+ 1085

10652

I actually think I've seen this exact problem in a MathCounts competition before...strange!

Nice, you got it

ReplyDeleteHEy chralie Guthrie can you tell me in a easy way i couldn't get this fully.

DeleteHi :)

ReplyDeleteActually I find exactly 155 solutions. Like so :

9000 + 1000 = 10000

9010 + 1090 = 10100

9110 + 1001 = 10111

9120 + 1091 = 10211

9220 + 1002 = 10222

9230 + 1092 = 10322

9330 + 1003 = 10333

9340 + 1093 = 10433

9440 + 1004 = 10444

9450 + 1094 = 10544

9550 + 1005 = 10555

9560 + 1095 = 10655

9660 + 1006 = 10666

9670 + 1096 = 10766

9770 + 1007 = 10777

9780 + 1097 = 10877

9880 + 1008 = 10888

9890 + 1098 = 10988

9900 + 1199 = 11099

9990 + 1009 = 10999

9001 + 1000 = 10001

9011 + 1090 = 10101

9111 + 1001 = 10112

9121 + 1091 = 10212

9221 + 1002 = 10223

9231 + 1092 = 10323

9331 + 1003 = 10334

9341 + 1093 = 10434

9441 + 1004 = 10445

9451 + 1094 = 10545

9551 + 1005 = 10556

9561 + 1095 = 10656

9661 + 1006 = 10667

9671 + 1096 = 10767

9771 + 1007 = 10778

9781 + 1097 = 10878

9881 + 1008 = 10889

9891 + 1098 = 10989

9901 + 1189 = 11090

9002 + 1000 = 10002

9012 + 1090 = 10102

9112 + 1001 = 10113

9122 + 1091 = 10213

9222 + 1002 = 10224

9232 + 1092 = 10324

9332 + 1003 = 10335

9342 + 1093 = 10435

9442 + 1004 = 10446

9452 + 1094 = 10546

9552 + 1005 = 10557

9562 + 1095 = 10657

9662 + 1006 = 10668

9672 + 1096 = 10768

9772 + 1007 = 10779

9782 + 1097 = 10879

9892 + 1088 = 10980

9902 + 1189 = 11091

9003 + 1000 = 10003

9013 + 1090 = 10103

9113 + 1001 = 10114

9123 + 1091 = 10214

9223 + 1002 = 10225

9233 + 1092 = 10325

9333 + 1003 = 10336

9343 + 1093 = 10436

9443 + 1004 = 10447

9453 + 1094 = 10547

9553 + 1005 = 10558

9563 + 1095 = 10658

9663 + 1006 = 10669

9673 + 1096 = 10769

9783 + 1087 = 10870

9893 + 1088 = 10981

9903 + 1189 = 11092

9004 + 1000 = 10004

9014 + 1090 = 10104

9114 + 1001 = 10115

9124 + 1091 = 10215

9224 + 1002 = 10226

9234 + 1092 = 10326

9334 + 1003 = 10337

9344 + 1093 = 10437

9444 + 1004 = 10448

9454 + 1094 = 10548

9554 + 1005 = 10559

9564 + 1095 = 10659

9674 + 1086 = 10760

9784 + 1087 = 10871

9894 + 1088 = 10982

9904 + 1189 = 11093

9005 + 1000 = 10005

9015 + 1090 = 10105

9115 + 1001 = 10116

9125 + 1091 = 10216

9225 + 1002 = 10227

9235 + 1092 = 10327

9335 + 1003 = 10338

9345 + 1093 = 10438

9445 + 1004 = 10449

9455 + 1094 = 10549

9565 + 1085 = 10650

9675 + 1086 = 10761

9785 + 1087 = 10872

9895 + 1088 = 10983

9905 + 1189 = 11094

9006 + 1000 = 10006

9016 + 1090 = 10106

9116 + 1001 = 10117

9126 + 1091 = 10217

9226 + 1002 = 10228

9236 + 1092 = 10328

9336 + 1003 = 10339

9346 + 1093 = 10439

9456 + 1084 = 10540

9566 + 1085 = 10651

9676 + 1086 = 10762

9786 + 1087 = 10873

9896 + 1088 = 10984

9906 + 1189 = 11095

9007 + 1000 = 10007

9017 + 1090 = 10107

9117 + 1001 = 10118

9127 + 1091 = 10218

9227 + 1002 = 10229

9237 + 1092 = 10329

9347 + 1083 = 10430

9457 + 1084 = 10541

9567 + 1085 = 10652

9677 + 1086 = 10763

9787 + 1087 = 10874

9897 + 1088 = 10985

9907 + 1189 = 11096

9008 + 1000 = 10008

9018 + 1090 = 10108

9118 + 1001 = 10119

9128 + 1091 = 10219

9238 + 1082 = 10320

9348 + 1083 = 10431

9458 + 1084 = 10542

9568 + 1085 = 10653

9678 + 1086 = 10764

9788 + 1087 = 10875

9898 + 1088 = 10986

9908 + 1189 = 11097

9009 + 1000 = 10009

9019 + 1090 = 10109

9129 + 1081 = 10210

9239 + 1082 = 10321

9349 + 1083 = 10432

9459 + 1084 = 10543

9569 + 1085 = 10654

9679 + 1086 = 10765

9789 + 1087 = 10876

9899 + 1088 = 10987

9909 + 1189 = 11098

You could have sent a different answer every week to your father, and get rich.

dude wtf cx

DeleteOr if every letter has to be a different digit, then you still have 21 solutions ;)

ReplyDelete9342 + 1093 = 10435

9452 + 1094 = 10546

9562 + 1095 = 10657

9672 + 1096 = 10768

9782 + 1097 = 10879

9453 + 1094 = 10547

9563 + 1095 = 10658

9673 + 1096 = 10769

9234 + 1092 = 10326

9564 + 1095 = 10659

9235 + 1092 = 10327

9345 + 1093 = 10438

9785 + 1087 = 10872

9236 + 1092 = 10328

9346 + 1093 = 10439

9786 + 1087 = 10873

9237 + 1092 = 10329

9567 + 1085 = 10652

9458 + 1084 = 10542

9568 + 1085 = 10653

9678 + 1086 = 10764

Half a year worth of pocket money...

Ooops... sorry, the previous comment is obviously wrong... there's only one solution with all the digits being different, and that's the one you gave. My mistake, humbly !

ReplyDeletedude f u fuckin bitch

Delete9235 + 1092 = 10327

ReplyDeleteIt is the Constraint Satisfaction Method (CSM) from the Science of Artificial Intelligence.

ReplyDeleteCan you teach us how to solve it? I need to show my work for a homework assignment and im confused...?

ReplyDeleteI'm not sure how Matt did it, but I did a plug and chug where I started with some assumptions for S and M in order to get an answer in the 10,000s. You can then slowly see the relationship of what the numbers would have to be, again with a little plug and chug. Actually, I tried a value for M as zero and found an answer of 3712 + 0467 = 04179

ReplyDeleteInterestingly my sister came up with the same result using M=0 before finding the result with M=1.

DeleteI argued that M=0 is invalid due to 0 being a placeholder and irrelevant in that slot (where there are theoretically infinite zeroes.) But it is an applause-worthy unconventional solution, and it does work!

i have

ReplyDelete2817+368=3185

2819+368=3187

3719+457=4176

3712+467=4179

3829+458=4287

3821+468+4289

5731+647=6378

5732+647=6379

5849+638=6487

6419+724=7143

6415+734=7149

6524+735=7259

6853+728=7581

6851+738=7589

7316+823=8139

7429+814=8243

7539+815=8354

7531+825=8356

7534+825=8359

7649+816=8465

7643+826=8469

8432+914=9347

8542+915=9457

and the last

9567+1085=10652

that's all.there is no other

thanks.bye

Two four-digit numbers cannot sum to more than 20,000 so M=1.

ReplyDeleteNow this sum must also be smaller than 12,000 so O=0.

Looking at the hundreds column, it must include a carry and N=E+1. There is no carry in the thousands column so S=9.

The sum in the tens column must satisfy N=E+1 and so R=8 and there is a carry.

The only sum in the units column that causes a carry and uses the remaining digits is D=7, E=5, Y=2.

So the solution is 9567+1085=10652.

why must it be smaller than 12,000?

Delete