England are none the wiser on who their third fast bowler will be in Brisbane after an underwhelming showing in Sydney.

England were hoping to solve their fast bowling conundrum in their final tour match in Sydney, but it seems the plot has only thickened six days out from the first Test.

Veteran seamer Chris Tremlett appears the safe option and the front runner for Brisbane, but the merits of Steven Finn’s five-wicket first innings haul against an Invitational XI at the SCG are sure to be debated by selectors.

England’s bowlers failed to fully impose themselves on day three in Sydney, with opener Aaron Finch smashing 59 from 60 balls as the Invitational XI went to stumps at 4-153 – a lead of 39.

Stuart Broad, Boyd Rankin, Graeme Swann and Finn took a wicket each, after Joe Root earlier posted 75 with the bat to power England’s first innings total to 418 – setting up a 114-run advantage at the change.

“It’s not ideal conditions for fast bowlers with the (sandy) run-ups and everything,” said Finch.

“I thought Finn’s spell towards the end with the old ball was outstanding. He found reverse swing, had it going around pretty well and the ball that knocked Callum Ferguson (26) over was ball of the day.”

As England grafted away on Friday, wicketkeeper Matt Prior worked hard on the training park and in the gym to try to overcome his calf injury.

The Ashes holders’ other injury concerns seem less severe, although Kevin Pietersen (knee) and Alastair Cook (back) both spent time off the field.

And after an initial scare where trainers rushed out to treat him in the middle, Root continued to bat and field despite copping a nasty hit on his right hand.

England’s batting is in order with Root the fourth top-order player to post a half-century in the SCG match, and every member of the top six has now scored either a hundred or 50 on tour.

No.2 wicketkeeper Jonny Bairstow contributed 48 in a 106-run stand with Root and said he’s ready to go with the gloves if Prior is ruled out.

“It’s filled me with confidence and if that opportunity does come along I do feel as though I’d do a decent job,” he said.

Finn has an excellent wicket-taking strike-rate – and took six first-innings wickets in 2010/11 at the corresponding Gabba opener.

But his record suggests he also leaks runs, and despite taking five wickets, his efforts on day one in Sydney were particularly lukewarm.

Tremlett averages 26.75 in Test cricket and used his great height to take 17 scalps in just three Tests last time England were in Australia.

But it’s been nearly two years since the 32-year-old played for England and his recent first-class record has been moderate.

James Anderson and Broad form a lethal duo to lead the attack, and for that reason England may favour Tremlett, rather than risk Finn being taken to the cleaners.

Finch entered the tour match against England fresh from a king pair in the Sheffield Shield, but the right-handed opener fought back on Friday – smashing 10 fours and a six – and vowing not to curb his all-out attacking approach.

“When you bat twice and face two balls … things can’t really get much worse, can they? That’s the way I was thinking about it,” Finch said.