Were Jesus’ disciples allowed to carry staffs?

When Jesus sent out his twelve disciples to proclaim the gospel, he told them to travel light. They were not to take money, nor a bag, nor a second tunic; instead, they were to rely on those to whom they preached to provide for their needs. This is recorded in all three of the synoptic gospels. However, they disagree as to whether Jesus allowed his disciples to carry a staff.

In Matthew, the prohibition on staffs is clear:

Take no gold, or silver, or copper in your belts, no bag for your journey, or two tunics, or sandals, or a staff; for labourers deserve their food. [Matthew 10:9-10 (NRSV)]

In Luke, Jesus is similarly against the carrying of staffs:

He said to them, ‘Take nothing for your journey, no staff, nor bag, nor bread, nor money–not even an extra tunic.’ [Luke 9:3 (NRSV)]

In Mark, however, Jesus lists a staff as the one thing that his disciples can take with them:

He ordered them to take nothing for their journey except a staff; no bread, no bag, no money in their belts; but to wear sandals and not to put on two tunics. [Mark 6:8-9 (NRSV)]

So were Jesus’ disciples allowed to take a staff with them or not?