Set-cover experiment · checked August 24, 2026
10passports

How many passports cover every tracked destination?

10 are necessary and sufficient under MultiPass Rank's easy-access rule. The result comes from an exact search, not a greedy estimate; below is one minimum set and the reason 9 cannot work.

One exact minimum set

From 189 destinations to all 227.

Passports are ordered by their marginal contribution within this solution, not by acquisition value or chronology.

  1. 01SpainESAdds+192Cumulative192
  2. 02United Arab EmiratesAEAdds+16Cumulative208
  3. 03TunisiaTNAdds+7Cumulative215
  4. 04RwandaRWAdds+3Cumulative218
  5. 05North KoreaKP · forcedAdds+2Cumulative220
  6. 06MaldivesMVAdds+2Cumulative222
  7. 07ChadTDAdds+2Cumulative224
  8. 08AfghanistanAF · forcedAdds+1Cumulative225
  9. 09EritreaER · forcedAdds+1Cumulative226
  10. 10YemenYE · forcedAdds+1Cumulative227

Complete set: Spain + United Arab Emirates + Tunisia + Rwanda + North Korea + Maldives + Chad + Afghanistan + Eritrea + Yemen

The lower-bound proof

4 passports are unavoidable.

Afghanistan, Eritrea, North Korea, Yemen each has only one passport in this snapshot that reaches it under the easy-access threshold: its own. Therefore every full-coverage solution must include all 4 of those passports. This does not mean other travellers cannot enter; their route is classified as an eVisa or traditional visa instead.

With those 4 fixed, the solver removes candidates whose easy-access destination set is a strict subset of another passport's set. It then uses exact branch-and-bound search on the remaining destinations. No combination of 5 additional passports succeeds. 6 do, proving a lower and upper bound of 10 in total.

Read the boundary carefully

A mathematical portfolio, not a citizenship plan.

“Covered” means citizenship, visa-free, ETA, or visa-on-arrival access. It does not mean every destination is literally visa-free. The experiment does not consider whether these citizenships can be acquired or retained together, nor tax, residence, work, military, consular, ethical, or administrative consequences.

The result reports one exact minimum solution; other 10-passport solutions may tie. Travel rules can change, so the snapshot date is part of the finding. See the scoring methodology before reusing the number.