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CREATE TABLE user_private_message (
id INT NOT NULL AUTO_INCREMENT PRIMARY KEY,
user_from_id INT NOT NULL,
send_time TIMESTAMP NOT NULL DEFAULT NOW()
);
INSERT INTO user_private_message(user_from_id, send_time)
VALUES
(1, '2007-01-01 00:00:00'),
(1, '2007-01-02 00:00:00'),
(2, '2007-01-02 00:00:00'),
(3, '2007-01-02 00:00:00'),
(1, '2007-01-03 00:00:00'),
(2, '2007-01-03 00:00:00'),
(3, '2007-01-03 00:00:00'),
(1, '2007-01-04 00:00:00'),
(2, '2007-01-04 00:00:00'),
(3, '2007-01-04 00:00:00'),
(1, '2007-01-05 00:00:00'),
(2, '2007-01-05 00:00:00');

Records: 12  Duplicates: 0  Warnings: 0
SELECT DISTINCT DATE(send_time)
FROM user_private_message
GROUP BY DATE(send_time), user_from_id
HAVING COUNT(user_from_id) = 1
LIMIT 1;
DATE(send_time)
2007-01-01