When a 3 digit number is added to a 4 digit number and the result is a 5 digit number then the highest digit of the 4 digit number must be 9 and the highest to of the result must be 10.
Y+O=9+4=13. There cannot be a carry from O+U. If there was a carry A would also be 4.
Because O+U doesn’t have a carry the result is less than 10.
It also can’t be 9 because then R would be 9 or 0 and those numbers are already used.
So U must be less than 5 and the only number remaining is 2.
R can either be 6 when there is no carry from U+R or 7 when there is.
Because U=2 there will be no carry with either number.
H+A+T+E = 1+3+8+0 = 12
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