draw a blank

draw a blank (fail)
You draw a blank when you attempt to recall something and fail, or when you try to come up with a solution to a problem and can't think of one.

потерпеть неудачу;
≅ (но) все впустую (т. е. не удалось добиться результата — найти, вспомнить, догнать, проч.);
≅ (вернуться) ни с чем;
≅ (вернуться) несолоно хлебавши {букв. вытянуть пустой лотерейный билет}

Example 1: She asked me for my phone number and I drew a blank—I couldn't remember it. — Она спросила мой номер, а я ну никак не мог его всомнить.

Example 2: He said we'd met before, but I just drew a blank (= I did not remember him).

Example 3: The police investigated the case, but drew a complete blank. — Полиция занималась расследованием дела, но все совершенно впустую; но ровным считем ничего не выяснили; совершенно никакого результата это не принесло.

Example : Well, he might be at his club, but if you draw a blank there, I don't know where can be. — Может, он и в клубе, как обычно, но если вы и там его не найдете, то я не знаю, где он может быть.

Origin
This expression finds its origins in Tudor England, when the first national lottery was established by Queen Elizabeth the First in 1567. The lottery worked by putting slips of paper with the participants names on them into a pot, while an equal number of slips, some with prizes on them and some left blank, were put into another pot. Pairs of tickets were drawn simultaneously from the pots, matching a participant to a prize. More often than not, however, a blank slip was drawn, and the participant won nothing! (ecenglish.com)