Timeout for a Martin Gardner puzzle

With my 10 year-old VN student today we took a break from Physics and Chemistry (vector diagrams with billiard balls was a bit too heavy and the webwhiteboard app was pretty awful) to look at one of Martin Gardner's simpler problems:
G O O D
+ T I M E
________
M A T H S

The ten letters each being different letters.
No leading zeroes of course, and there are several answers.
Care to try your hand at it? Note that D and E are interchangeable but we don't care.
What is the number represented by MATHS? Can you find more than one solution?
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Comments (5)

No takers huh? It's not easy because only two digits appear twice, O and M. There are in fact four solutions, and of course a Python sledge hammer would get you there quickly.
Let's get the ball rolling:
There can be four carries C1 (right), C2, C3, C4 (left)
M is obviously 1, C4=1 and G+T+C3 >=10
D+E may generate C1 (0 or 1)
O+M+C1 may generate C2 (0 or 1)
O+I+C2 may generate C3 (0 or 1)
G+T+C3 >=10 so C4 =1 and M = 1
All ten digits are present and all are different.
D,E,G,T,M,O are all non-zero.
(If O is zero C1=1, else H=M and C2=0 so that I=T - O is also not 0)
There was a hint in one article: O=3 but I'd prefer to find it myself.
One way to solve is to make a table and eliminate where possible
0 1 2 3 4 5 6 7 8 9
A _ X _ X _ _ _ _ X X
D X X X _ _ _ _ _ _
E X X X _ _ _ _ _ _
G X X X X _ _ _ _ _ _
H _ X X _ _ _ _ _ _
I _ X X _ _ _ _ _ _
M X Y X X X X X X X X
O X X X Y X X X X X X
S _ X _ X _ _ _ _ _ _
T X X _ X _ _ _ _ _ _
C1 _ _
C2 _ _
C3 _ _
C4 X Y
Note that:
D+E=S+10*C1
O+M+C1=H+10*C2
O+I+C2=A+10*C3
G+T=A+10
A<G, A<T, A<=7 ==> G,T > 3
I don't have python skills (at least not in that sense); but other maths blogs are good....

thumbs up
We see G and T are interchangeable, so we can arbitrarily choose G < T
Likewise for D and E, so choose D < E
That guarantees at least four solutions if there is one.
This is one that does not need a computer, but perseverance and deduction and elimination
Whoops G and T cannot be switched because T occurs twice, just D and E
It seems clear O can be 8 or 4, not just 3
A quickie python tells me
1 5884 6719 12603
1 5889 6714 12603
2 7336 2918 10254
2 7338 2916 10254
3 7443 2816 10259
3 7446 2813 10259
But an article claims also 16750 - ah found it, G could be 9 after all!
4 9332 7418 16750
4 9338 7412 16750
But the idea was to do this mentally
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FargoFan

sydney, New South Wales, Australia

Retired but teaching and studying every day, travelling whenever I can and at home wherever I happen to be. From a small family but wishing I were part of a larger one. My students are scattered all over the world, as is my family. Language is a part [read more]