Postgres 10

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Help with an interesting Postgres question: Why isn't an Index Only Scan used on a partition accessed via the parent table?.

CREATE table illness (nature_of_illness VARCHAR(25), created_at TIMESTAMP);

INSERT INTO illness VALUES ('Cervix', '2018-01-03 15:45:40');
INSERT INTO illness VALUES ('Cervix', '2018-01-03 15:45:40');
INSERT INTO illness VALUES ('Cervix', '2018-01-03 15:45:40');
INSERT INTO illness VALUES ('Cervix', '2018-01-03 15:45:40');
INSERT INTO illness VALUES ('Cervix', '2018-01-03 15:45:40');
INSERT INTO illness VALUES ('Lung',   '2018-01-03 17:50:32');
INSERT INTO illness VALUES ('Lung',   '2018-02-03 17:50:32');
INSERT INTO illness VALUES ('Lung',   '2018-02-03 17:50:32');
INSERT INTO illness VALUES ('Lung',   '2018-02-03 17:50:32');
INSERT INTO illness VALUES ('Cervix', '2018-02-03 17:50:32');
-- 2017, with 1 Cervix and Lung each for the month of Jan - tie!
INSERT INTO illness VALUES ('Cervix', '2017-01-03 15:45:40');
INSERT INTO illness VALUES ('Lung',   '2017-01-03 17:50:32');
INSERT INTO illness VALUES ('Lung',   '2017-02-03 17:50:32');
INSERT INTO illness VALUES ('Lung',   '2017-02-03 17:50:32');
INSERT INTO illness VALUES ('Lung',   '2017-02-03 17:50:32');
INSERT INTO illness VALUES ('Cervix', '2017-02-03 17:50:32');

1 rows affected

1 rows affected

1 rows affected

1 rows affected

1 rows affected

1 rows affected

1 rows affected

1 rows affected

1 rows affected

1 rows affected

1 rows affected

1 rows affected

1 rows affected

1 rows affected

1 rows affected

1 rows affected

Year	Month	Tumour count	Type
2017	1	1	Cervix
2017	1	1	Lung
2017	2	3	Lung
2018	1	5	Cervix
2018	2	3	Lung