## Wednesday, August 18, 2010

### SEND MORE MONEY

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

1. After several hours of vigorous problem solving and guess-and-check, I think I've come upon the solution.
9567
+ 1085
10652
I actually think I've seen this exact problem in a MathCounts competition before...strange!

2. Nice, you got it

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

3. Hi :)

Actually 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.

1. dude wtf cx

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

9342 + 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...

5. 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 !

1. dude f u fuckin bitch

6. 9235 + 1092 = 10327

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

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

9. I'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

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

I 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!

10. i have
2817+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

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

Now 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.

1. why must it be smaller than 12,000?

12. thank for good post and sharing.......

goldenslot
สูตรบาคาร่า

13. Your blog is very useful for me.I really like you post.Thanks for sharing.

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