# One to Eleven Sum to Twenty Five

From the picture shown below, deduce the missing numbers (one to eleven)... none of them repeating.

Four Numbers surrounding the Five diamonds A, B, C, D, E, as well as the five numbers in the outer circle, all add up to 25. Three numbers: 7, 5, 1 are already filled in.

• This is an interesting puzzle! There's a nice logical path to a single solution with a clever "break-in" step at the start. I'd love to see more creative deduction-based puzzles like this (and less number sequences). – Deusovi Jun 16 at 10:28
• Getting there..I am trying to mixup various genres compared to when I started. – Uvc Jun 16 at 10:39

Full Solution

Notation:

## Deducing $$e$$

sum of 1 to 11 is 66. each circle is counted to sum 25 twice, except that in the middle, which is counted 5 times.

therefore,

$$66+66-2*e+5*e=25*6$$
$$132+3*e=150$$
$$e=6$$

## Deducing $$c, f, h$$

regarding B, C:

$$c+4=h$$

only pair available for distance of 4 is:

$$4 & 8$$

Therefore,

$$c=4, h=8$$

Sum of 25 rule renders

$$f=10$$

## Deducing the rest

regarding A, E:

$$d+2=a$$

only pair available for distance of 2 is:

$$9 & 11$$

Therefore,

$$d=9, a=11$$

Sum of 25 renders

$$b=3, g=2$$

• Great!,,,got it... – Uvc Jun 16 at 9:29