Draw a blank
To fail to recall a memory or fail in some speculative effort.
This phrase originates from the lottery that was established in Tudor England. Elizabeth I, like the monarchs of other European countries at the time, was short of money and decided to copy rival nation states by instituting a national lottery. The money so raised was intended to go towards the 'reparation of the havens and strength of the Realm and towards further public works'. She signed the license granting the lottery in 1567 (not so much a signature, more a craft project).
Lotteries at that time worked by putting tickets with the participant's names on them into a 'lot pot'. An equal number of notes, some with the prizes written on them and some of which were blank, went into another pot. Pairs of tickets were drawn simultaneously from the two pots. It is easy to see how a failure to succeed came to be associated with drawing a blank.
Sir William More (1520-1600), when he found time to spare from his numerous other posts, which included 'Her Majesty's Deputy Master of the Swans', was the 'Treasurer of the Lottery in Surrey'. The Loseley Manuscripts are a unique archive of the More-Molyneux family who have for centuries lived in the beautiful Tudor manor house Loseley Park. The manuscripts contain a unique record of life in Tudor and Stuart England and include More's description of the lottery:
"A verie rich Lotterie ... without any blancks."
And so it should have been. The tickets cost ten shillings each - at a time when labourers were paid about a shilling a day. The prizes included silver plate and tapestry.
Although the first time that someone 'drew a blank' was in the 16th century, the phrase wasn't recorded in print until the 19th, in Washington Irving's Tales of a Traveller, 1824, in which the plot involves a character being given credit for something he hadn't done:
"It is like being congratulated on the high prize when one has drawn a blank."
Soon after that date the phrase began to be used in hunting circles; for example, from the 1832 Hunting Songs by the impressively named Rowland Eyes Egerton-Warburton:
"The man - whose heart heaves a sigh when his gorse is drawn blank."
Later in the 19th century it became used in a general figurative sense to mean to be unsuccessful in a venture or search of any kind.