Sudoku Players' Forum (clone)

Link to puzzle - https://ibb.co/2ZjCZ7f

r4c467 add up to 23
must be {6,8,9}

70 minutes in. Still super stuck. Am i missing something obvious?

https://ibb.co/L9cwZRN

In box 6, 1 & 3 are in R5C7 and either R4C8 or R4C9 so they can be eliminated from the rest of the box. This leaves R6C6 as just 1 & 3.

thelardoffear wrote:This leaves R6C6 as just 1 & 3.

why can't the 3-cell cage with sum=10 be 1,4,5 and so r6c6 is different ?

Hajime wrote:

thelardoffear wrote:This leaves R6C6 as just 1 & 3.

why can't the 3-cell cage with sum=10 be 1,4,5 and so r6c6 is different ?

the 3-cell cage must contain a 1 or a 3.
(including your example.)

the 1 or 3
is not in b6!

r6c7 + r6c8 are not 1 and 3 so their minimum values would be 2 & 4 so the last cell in the cage r6c6 has to be less than 4 (10 - 4 - 2) but obviously it can't be 4 if it is elsewhere in the same cage and 2 has already been eliminated so r6c6 can only be 1 or 3.

Also to clarify my original step
if r5c7 = 1 then r4c8 & r4c9 would be 3 & 5
if r5c7 = 3 then r4c8 & r4c9 would be 1 & 7

so 1 & 3 can be eliminated from the rest of box 6.

or this way:

in b6,
the cage of 8
is either {1,7} or {3,5}

so, it must include
either 1 or 3

; with r5c7,
this takes the {1,3} for b6



the cage of 10 in r6
must include a 1 or 3
(the minimum without them is 2+4+5 > 10),

- and it must be outside b6