perplexus.info :: Numbers : The magnificent twelve

The magnificent twelve (Posted on 2017-04-07)

Z+E+R+O = 0
O+N+E = 1
T+W+O = 2
T+H+R+E+E = 3
F+O+U+R = 4
F+I+V+E = 5
S+I+X = 6
S+E+V+E+N = 7
E+I+G+H+T = 8
N+I+N+E = 9
T+E+N = 10
E+L+E+V+E+N =11
T+W+E+L+V+E = 12

Solve the above system of alphametics, allowing non-zero integers, whose absolute value does not exceed 11.

Rem 1: The source will be disclosed with the official solution.
Rem 2: An analytical solution (d4) will be applauded!

Submitted by Ady TZIDON

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Solution: (Hide)

Z+E+R+O = 10 + 3 – 6 – 7 = 0
O+N+E = –7 + 5 + 3 = 1
T+W+O = 2 + 7 – 7 = 2
T+H+R+E+E = 2 + 1 – 6 + 3 + 3 = 3
F+O+U+R = 9 – 7 + 8 – 6 = 4
F+I+V+E = 9 – 4 – 3 + 3 = 5
S+I+X = –1 – 4 + 11 = 6
S+E+V+E+N = –1 + 3 – 3 + 3 + 5 = 7
E+I+G+H+T = 3 – 4 + 6 + 1 + 2 = 8
N+I+N+E = 5 – 4 + 5 + 3 = 9
T+E+N = 2 + 3 + 5 = 10
E+L+E+V+E+N = 3 + 0 + 3 – 3 + 3 + 5 = 11
T+W+E+L+V+E = 2 + 7 + 3 + 0 – 3 + 3 = 12

See my post allowing represantation of the zero digit by O

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Better late than never!	Ady TZIDON	2020-04-15 04:47:13
a d2 sequel - with a hint	Ady TZIDON	2017-04-10 07:05:13
computer solution (spoiler) -- with a caveat on the restrictions	Charlie	2017-04-07 12:26:51

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