# Four Rings & Seven Digits Replace a to f with the numbers 1 to 2 & 4 to 7, so that the sum inside each ring is the same. There is only one solution!

• If there is more than one solution, your question will be flagged as too broad!
– A.D.
Jun 18, 2015 at 16:40
• Here's a suggestion: Pick one of the solutions and think of an additional rule or pattern that they must follow. That would help narrow down the possibilities. Jun 18, 2015 at 16:49
• Or possibly ask for a generic solution which can be applied to find all possible solutions. Jun 18, 2015 at 16:50
• There were four equations to start with, and seven variables. You need to have at least one equation per variable in order to have a unique solution. The current version is 4 & 6, so there's still potentially multiple. Jun 18, 2015 at 17:24
• As far as I can tell, this is now a unique solution. I've voted to reopen. Jun 18, 2015 at 17:33

a=6; b=4; c=5; d=1; e=2; f=7

And

The sum is 10 in each circle

Blue circle equals purple, so

d+e+f=3+f
d+e=3 (they must equal 1 and 2)


and

d+e+f=b+c+d
e+f=b+c

• e has a maximum value of 2
• Only 4-7 remain, so b+c has a minimum value of 9 (4+5)
• This constrains f to be 7 and e to be 2, leaving d to be 1.
• The total per circle is then 10 and 6 is the only value left for a, so b is 4 and c is 5.

Giving us:

a=6, b=4, c=5, d=1, e=2, f=7