Alphanumeric puzzle can you solve it? ONE+TWO+FIVE=EIGHT?

Answer 1

(@ ksoileau... In your solution, N = H = 2; in puzzles like this, you can't use the same digit twice...)

Since the E is the result of carry, E = 1.
The sum of three digits (even plus carry) can't be more than 29, so I can be 0 or 1. If different letters are different digits, I = 0. This gives

The hundreds give O + T + I + carry = G, which is at most 9 + 8 + 0 + 2 = 19, so there can be at most 1 carried over to the thousands. Therefore, F = 9.

ON1 = TWO + 90V1 = 10GHT

It is clear that O + 2 = T. There can't be carry here because that would make T = 0 or 1, which have been used already. In the thousands, we find the sum O + T [+ 0], which is equal to 2(O + 1), and therefore even. Since there is a carry to F, this sum must be 10 or greater, so that possible values for O and T are (4, 6), (5, 7) and (6, 8).

CASE I
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4N1 + 6W4 + 90V1 = 10GH6 gives G = carry over from N + W + V, which must be 2. Combined with H >= 3, this gives N + W + V >= 23. Since 8 + 7 + 6 = 21 is too small, this can't be done.

CASE II
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5N1 + 7W5 + 90V1 = 10GH7
G = 2 + carry over from N + W + V; this sum is at most 8 + 6 + 4 = 18; it is at least 2 + 4 + 6 = 12. Therefore, G = 3.

However, the remaining digits are 2, 4, 6 and 8, with sum 20. Since N + W + V = 10 + H, both sides must be equal to half of (10 + 20), making H = 5 -- impossible.

CASE III
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6N1 + 8W6 + 90V1 = 10GH8
G = 4 + carry over from N + W + V, which is at most 7 + 5 + 4 = 16, and at least 2 + 3 + 4 = 9. This makes G = 4 or G = 5. However, G = 4 is impossible because that would require the 4 to show up in the sum 2 + 3 + 4 as well. Conclusion: G = 5.

The remaining numbers are 2, 3, 4 and 7, for a total of 16.
Also, N + W + V = H + 10, and the sum of both sides of this equation is 26. Therefore, both sides equal 13, and H = 3. The remaining numbers -- 2, 4, 7 -- can be assigned to N, W, V in any order.

621 + 846 + 9071 = 10538
641 + 876 + 9021 = 10538
671 + 826 + 9041 = 10538
621 + 876 + 9041 = 10538
641 + 826 + 9071 = 10538
671 + 846 + 9021 = 10538

Thus I have proven that these are the only six solutions.

Answer 2

Alphanumeric Puzzles

Answer 3

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Lots of tips: 1) I go for the first letter of a word up and then down - if I can get one of the two words, then having the first letter of the other sometimes jogs my memory. 2) Sometimes, it doesn't have to be the first letter. 3) Paying attention to the theme of the crossword, if any, is helpful. 4) Go for the easier ones first, then more difficult. 5) Reference: computer, dictionary, thesaurus, atlas, etc... 6) Having someone help you. 7) Going away and coming back to it later can sometimes clear the mind and help one focus better. 8) Going back to other crosswords. 9) Enjoy what you are doing. 10) Use a pencil on ones you're not sure of. 11) Place a checkmark next to the number of the hints you've gotten - it can help you focus more on the ones you haven't gotten yet. 12) If it's in a book or newspaper, sometimes the answers can be found in the publication that the crossword is in. 13) etc... 14) sometimes the answers just come out of no where - be patient. 15) sometimes working on a section of the puzzle (upper left, right or lower left or right. 16) thinking about the hint or hints with a different perspective.

Answer 4

621
836
9071
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10528