Puzzle no. 1 - Going on Eighteen. [solution]
This is an old mathematical puzzle, but one I thought many of you might enjoy.
The task is simple: Arrange the numbers 1 through 10 in the boxes. The sum of each row (down and across) must equal 18.
There are several solutions to this puzzle.
Your answer should look something like this:
|1|2|3|4|
|5|x|x|6|
|7|8|9|10|
Or, if you wish to draw the answer (or show all your puzzling work), that's alright too.
For those of you who can only hear this message, the boxes are arranged in a rectangle, with four boxes on the top and bottom, and three boxes on each side. There should be ten boxes total.
Posts will be screened until around this time tomorrow, to prevent people who have solved the puzzle from spoiling it for those who haven't.-- TIME IS UP! btw drop a post in my journal if you think there's another way to handle the solutions, or if posting them after time has passed is a good method.
Solution:
First, let's find out what we know by assigning each place in the puzzle a letter.
A - B - C - D
E - - - - - F
G - H - I - J
The puzzle states that each row = 18.
A+B+C+D = 18
A+E+G = 18
D+F+J = 18
G+H+I+J = 18
Since A through J are the letters 1 through 10, we can add them together.
We know, then, that A+B+C+D+E+F+G+H+I+J = 55
Also, since A+B+C+D = 18, and G+H+I+J = 18, the two remaining letters, E+F, must equal 19. The only two numbers that can equal 19 are 10+9.
Therefore,
E = 9 and F = 10.
Now we know where our 9 and 10 go!
A - B - C - D
10 - - - 9
G - H - I - J
From there, we need to find what combinations will add up to 18 using the numbers 9 and 10.
There are only a few. We only need to look for the combinations in 3.
10+1+7
10+2+6
10+3+5
9+1+8
9+2+7
9+3+6
9+4+5
We know that certain combinations won't work (like ones that share a number, so we can pair the ones what will)
10+1+7 - 9+3+6, 9+4+5
10+2+6 - 9+1+8, 9+4+5
10+3+5 - 9+1+8, 9+2+7
From there it's a matter of guess and check, but we only have six possible combinations (much less than the number we were working with before!) The final answer should look something like this:
6 - 4 - 7 - 1
10 - - - 9
2 - 5 - 3 - 8
You can use the same method for other "mystic square" puzzles, making a frustrating guessing game a solvable problem. Every puzzle has an answer!
The task is simple: Arrange the numbers 1 through 10 in the boxes. The sum of each row (down and across) must equal 18.
There are several solutions to this puzzle.
Your answer should look something like this:
|1|2|3|4|
|5|x|x|6|
|7|8|9|10|
Or, if you wish to draw the answer (or show all your puzzling work), that's alright too.
For those of you who can only hear this message, the boxes are arranged in a rectangle, with four boxes on the top and bottom, and three boxes on each side. There should be ten boxes total.
Posts will be screened until around this time tomorrow, to prevent people who have solved the puzzle from spoiling it for those who haven't.-- TIME IS UP! btw drop a post in my journal if you think there's another way to handle the solutions, or if posting them after time has passed is a good method.
Solution:
First, let's find out what we know by assigning each place in the puzzle a letter.
A - B - C - D
E - - - - - F
G - H - I - J
The puzzle states that each row = 18.
A+B+C+D = 18
A+E+G = 18
D+F+J = 18
G+H+I+J = 18
Since A through J are the letters 1 through 10, we can add them together.
We know, then, that A+B+C+D+E+F+G+H+I+J = 55
Also, since A+B+C+D = 18, and G+H+I+J = 18, the two remaining letters, E+F, must equal 19. The only two numbers that can equal 19 are 10+9.
Therefore,
E = 9 and F = 10.
Now we know where our 9 and 10 go!
A - B - C - D
10 - - - 9
G - H - I - J
From there, we need to find what combinations will add up to 18 using the numbers 9 and 10.
There are only a few. We only need to look for the combinations in 3.
10+1+7
10+2+6
10+3+5
9+1+8
9+2+7
9+3+6
9+4+5
We know that certain combinations won't work (like ones that share a number, so we can pair the ones what will)
10+1+7 - 9+3+6, 9+4+5
10+2+6 - 9+1+8, 9+4+5
10+3+5 - 9+1+8, 9+2+7
From there it's a matter of guess and check, but we only have six possible combinations (much less than the number we were working with before!) The final answer should look something like this:
6 - 4 - 7 - 1
10 - - - 9
2 - 5 - 3 - 8
You can use the same method for other "mystic square" puzzles, making a frustrating guessing game a solvable problem. Every puzzle has an answer!