bonanova 85 Posted June 20, 2019 Report Share Posted June 20, 2019 OK these subtractions do not work using letters. But make a number substitution, the same for both, and everything's fine. N I N E N I N E - T E N - O N E ======= ======= T W O A L L Quote Link to post Share on other sites

1 Solution EventHorizon 15 Posted June 22, 2019 Solution Report Share Posted June 22, 2019 Spoiler L=0 (since E-E=L) N=1 (since the largest two three-digit numbers can sum to is 1998) A+O = 10 + I (A+O need to have a carry of 1 to make the 4 digit number) O+1=E W+E=11 (since N is 1, W+E would be too much so we need to borrow from the next) 2*T = I + 9 (since we borrowed above and the 1000's place has a 1), also I is odd. O+1=E and W+E=11 => W+O=10 A+O = (W+O) + I => A=W+I Since I is odd and the smallest W could be is 2, I is at most 7, but could be 5 or 3, too. Assume I = 7. 2T=9+7 = 16, so T=8. A=W+I => A=W+7, so A=9 and W=2. 10=W+O => 10=2+O => O=8, same as T. Assume I=5. T=(9+5)/2=7 ---> Assume A=9. 9=W+5 => W=4. 10=4+O => O=6. E=6+1=7, same as T ---> Assume A=8. 8=W+5 => W=3. 10=3+O => O=7, same as T ---> A can't be 7 (T is), and W needs to be at least 2 (0 and 1 are taken), so done here. Assume I=3. T=(9+3)/2=6 ---> A can't be 9, it would make W = 6, same as T. A can't be 6, it would make W=I. A can be 8,7,or 5. ---> Assume A=8. 8=W+3 => W=5. 10=5+O => O=5, same as W ---> Assume A=7. 7=W+3 => W=4. 10=4+O => O=6, same as T ---> Assume A=5. 5=W+3 => W=2. 10=2+O => O=8. E=8+1=9. Looks like this is the only solution. So L=0, N=1, W=2, I=3, A=5, T=6, O=8, E=9. NINE-TEN=TWO => 1319-691=628 NINE-ONE=ALL => 1319-819=500 Quote Link to post Share on other sites

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## bonanova 85

OK these subtractions do not work using letters.

But make a number substitution, the same for both,

and everything's fine.

N I N E N I N E

- T E N - O N E

======= =======

T W O A L L

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