Tuesday's games include the visit of Hearts to Cowdenbeath and Dundee United to Stenhousemuir while St Johnstone travel to Montrose and Livingston host Ayr United.
SPFL newcomers Cove Rangers face Dundee at the Balmoral Stadium on Wednesday while Clyde take on Hamilton Accies at Ochilview, with Broadwood unavailable because of the new artificial surface being laid.
Any group games ending in a draw are decided on penalties, with the shoot-out winners receiving a bonus point.
The eight group winners and four best runners-up join Celtic, Rangers, Kilmarnock and Aberdeen in the last 16, with the draw to be made on Sunday July 28.
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