Crossword puzzle- Crossnumber puzzle The puzzle below is a cross number puzzle, similar to a crossword puzzle except that the entries are numbers. Enter one digit per square. The thick heavy line is a separator.
ACROSS:
a. A prime number
c. The sum of digits of a across
DOWN:
a. Square of the sum of the digits of b down
b. A prime number
I am confused on how to solve this problem.
I do understand from across problem a must be a prime number so
a= 2, 3, 5 or 7. It can't be anything higher because it has to be one digit.
c is sum of digits of a and b across. Since it can only be one digit, c must be
c= 2, 3, 4, 5, 6, 7, 8, or 9
Then for down, the square of the sum of digits of b down would equal a, so (b+c)^2 is going to equal a down. However, does the box under a and across from c - will it have a number too?
I think it would have to because two numbers squared can't equal any of the above digits...
Finally B is a prime number so
b= 2, 3, 5, or 7
Unsure of where to go from here, because there are so many different paths to attempt and I am unsure of where to go from here.


1 step) a. across should be a prime number, which digit sum (c. across) is a 1 digit number.
2 step) c. across should be an odd number, because b. down is a prime number and can't be divisible by 2.
3 step) from step 2 -> a. across should be a prime number, which digit sum (c. across) is odd number.
4 step) from 1 and 3 steps -> a. across first digit should be even, because second digit is always odd for their sum to be odd.
5 step) from 1 and 4 steps -> we get two numbers which satisfy the rules, it is 43 or 61. So in b. down we get 37 or 17.
6 step) a. down is a square of the sum of the digits of b. down, so from step 5 -> we get a. down is 100 or 64.
7 step) 100 doesn't fit to our rules, 64 does.
Answer:
6 1
4 7

