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27 tickets that guarantee a UK Lotto win

Whatever six numbers come up, at least one of these 27 Lotto tickets matches two of them. Two University of Manchester mathematicians, David Cushing and David Stewart, proved in 2023 that 27 is the fewest that can do it: no set of 26 tickets works.

What the 27 tickets win

Since June 2026 every £2 Lotto line plays two rounds a draw, each with its own six numbers, and two matching numbers pay £1 in each round. The guarantee holds in each round, so 27 lines, £54 a draw, always win at least £1 in each round: £2 back, at minimum.

Bigger wins can happen too, as with any tickets, but nothing more is guaranteed. On average, 27 lines win about £20 a draw in prizes below the jackpot, so you'd expect to lose about £34 every draw.

The guarantee is also less special than it sounds: 27 random Lucky Dips already include a two-number match in a round 95% of the time. The wheel turns 95% into 100%. It doesn't change what you win on average; no choice of tickets can.

The 27 tickets

Mark these on 27 lines. They cover every number from 1 to 59.

  1. 01 02 03 04 05 06
  2. 01 02 03 04 07 08
  3. 01 02 05 06 07 08
  4. 09 10 11 12 13 14
  5. 09 10 11 15 16 17
  6. 12 13 14 15 16 17
  7. 18 19 20 21 24 25
  8. 20 21 22 23 26 27
  9. 22 23 24 25 28 29
  10. 24 25 26 27 30 31
  11. 18 19 26 27 28 29
  12. 20 21 28 29 30 31
  13. 18 19 22 23 30 31
  14. 32 33 34 35 38 39
  15. 34 35 36 37 40 41
  16. 36 37 38 39 42 43
  17. 38 39 40 41 44 45
  18. 32 33 40 41 42 43
  19. 34 35 42 43 44 45
  20. 32 33 36 37 44 45
  21. 46 47 48 49 52 53
  22. 48 49 50 51 54 55
  23. 50 51 52 53 56 57
  24. 52 53 54 55 58 59
  25. 46 47 54 55 56 57
  26. 48 49 56 57 58 59
  27. 46 47 50 51 58 59

Open in the playslip guide

Why they always work

Split the 59 numbers into five groups: 1–8, 9–17, 18–31, 32–45 and 46–59. Six numbers can't land in five groups without two of them sharing a group. So it's enough for every two numbers in the same group to be on a ticket together:

  • 1–8: three tickets. Treat the numbers as four pairs (1 and 2, 3 and 4, 5 and 6, 7 and 8). Each ticket holds three of the pairs, so any two pairs share a ticket.
  • 9–17: three tickets. Split them into three threes; each ticket holds two of the threes.
  • 18–31, 32–45 and 46–59: seven tickets each, from the Fano plane, a pattern of seven points and seven lines in which any two points lie on a line. Each point stands for two numbers, and each line of three points makes a ticket of six.

That's 3 + 3 + 7 + 7 + 7 = 27. Building 27 is the easy part. Cushing and Stewart's achievement was proving that 26 can never be enough, which took a careful computer-assisted proof.

The mathematicians tried it

When their paper came out, two numbers won a free Lucky Dip. Having noticed that their 27 tickets would have won £1,810 in the draw of 21 June 2023, Cushing and Stewart bought them for the draw of 1 July 2023. Three tickets matched two numbers, and the three Lucky Dips they won came to nothing. In their words, the £54 loss "serves both as a verification of our result and of the principle that one should expect to lose money when gambling."

Should you play them?

Only if a guaranteed small win is worth a near-certain loss to you. The 27 tickets also cover every number, so there's no room for numbers you like. A match-2 wheel does the same job for your own numbers, more cheaply: 10 tickets guarantee two matching numbers whenever two of your 15 are drawn, and 16 tickets guarantee two matching numbers whenever two of your 20 are drawn. Make a Lotto wheel to see how often each guarantee comes into play, or read how wheels work.

Source: David Cushing and David I. Stewart, "Applying constraint programming to minimal lottery designs" (2023), Remark 1.3 and Table 3. Their own 27 tickets are in its Table 4; ours are built the same way, numbered in order, and our software has checked them against all 45,057,474 possible draws. Prizes and prices are from the National Lottery's Lotto rules; always check the official results.