# 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= 1 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 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= 1 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.

• This is intriguing to say the least. I'm not aware of a simple way to do this without writing a program to do it. I'd love to see others' attempts. – Cameron Williams Mar 24 '14 at 1:10

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.

6 1
4 7


I have to do this problem for a math class. My teacher said that A across is a 2 digit number meaning the box that has an A in it and the box that has a B in it as well. I was not able to figure out the answer yet but I believe that A across must be either 43 or 61 making B down either 37 or 17. Hope this helped!

• Welcome to math SE. Please don't use answers if you are not providing a real answer to the problem – rlartiga Mar 25 '14 at 1:10

This is a crossword. I think you haven't paid much attention to the rule "The thick heavy line is a separator."

This means that:

• a word cannot pass through this heavy line
• a word cannot stop unless it finds either a heavy line OR the outer border of the crossword.
• a word cannot begin in the middle of the crossword. There should be a heavy line or a border before. This is the reason why there must not be a definition for "b across" or "c down".

Each square can contain only one digit. This, however, does not mean that "a across" should only fill the first square. The rule (eg for a across) is that:

• it should begin from the square named "a"
• it should continue to the right (if it was vertical/down it should continue down)
• until it finds a heavy line or the border.

So, "a across" is a 2-digit number, "c across" is 1 digit, "a down" and "b down" are 2 digits each.

Can you continue from now on?