Step 1: Combining clues from A1, E2, and B4 we can figure out what B2 and E4 are. Because every swimmer is underwater at least 2 times consecutively, and swimmers can’t go from being out of the pool to underwater directly, Swimmers 2 and 4 only have a few options of when they can can under water. Swimmer #2 can be underwater in A2, B2, and C2. B2 must be underwater or it is not possible for Swimmer 2 to be underwater two consecutive times. Similarly, Swimmer 4 must be underwater in E4.

Step 2: B2’s clue says, ‘Exactly one swimmer was in the pool for three consecutive time slots.’ The only possible swimmers that could do this are #3 and #5. F5’s clue says, ‘Exactly one swimmer was underwater four times.’ The only possible swimmers that could do this are Swimmers 3 and 5. The only order in which a swimmer can be underwater four times is U, U, U, U, I, O (or reversed). The only order in which a swimmer can be in the pool for three consecutive slots is U, U, I, I, I, O (or reversed). Notice that 4 out of the 6 answers are the same for these two columns. Because Swimmer 5 is already out of the pool for the sixth time slot, E5 must be in the pool, and A5 & B5 must be underwater. C5 and D5 we leave blank because they are either both underwater or both in the pool.

Step 3: E4’s clue says, ‘Exactly one swimmer was out of the pool for three consecutive time slots.’ This swimmer cannot be Swimmer 3 or 5 because those are the swimmers that fulfill B2 and F5’s clues. This swimmer cannot be Swimmer 1 because it isn’t possible for Swimmer 1 to be out of the pool 3 consecutive times. This means that Swimmer 2 or Swimmer 4 is the swimmer that is out of the pool three consecutive times.

Now let’s look at cell A3. A3 is either underwater or out of the pool, because we already know that Swimmer 3 has to be U, U, _, _, I, O or O, I, _, _, U, U. Let’s see if A3 can be out of the pool. A5’s clue says, ‘At any given time slot at least three swimmers are doing the same thing.’ If A3 is out of the pool this would mean both A2 and A4 would have to be in the pool. There is no other way to have three swimmers doing the same thing in the first time slot if A3 is out of the pool. If both A2 and A4 are in the pool, then it’s not possible for either Swimmer 2 or 4 to be out of the pool for three consecutive time slots. This means that A3 cannot be out of the pool and must be underwater. Knowing A3 is underwater also tells us that B3 is underwater, E3 is in the pool, and F3 is out of the pool.

Step 4: A5’s clue helps us fill in a few more spaces. We already determined that A2 and A4 cannot both be in the pool. This means that at least three swimmers were underwater in the first time slot. A4 cannot be underwater so the third underwater in the first row must be A2. In the fifth time slot (row 5), E1 must be in the pool to fulfill A5’s clue. With E1 being in the pool, F1 must be out of the pool, because there’s no other time in which Swimmer 1 could be out of the pool.

Step 5: For Swimmer 1 to be underwater for at least two consecutive time slots, C1 must be underwater. F1’s clue says, ‘Swimmers 4 and 4 were never doing the same thing at the same time.’ We know that at least one of C4 or D4 must be in the pool because B4 is out of the pool and E4 is underwater. We know that C5 and D5 are either both in the pool or both underwater. Because of F1’s clue C5 and D5 cannot both be in the pool so C5 and D5 must both be underwater. This means that Swimmer 3 is the simmer that was in the pool for three consecutive time slots, so C3 and D3 are both in the pool. D4 cannot be out of the pool (B4’s clue) and cannot be underwater (F1’s clue), so D4 must be in the pool. This means that F4 must be underwater (E2’s clue).

Step 6: D4’s clue says, ‘Swimmers 1 and 2 were underwater for a different number of time slots.’ This means that out of Swimmers 1 and 2, one was underwater three times and one was underwater two times. Let’s try Swimmer 2 being underwater three times. This would mean that C2 is underwater and D2 is in the pool. This would mean Swimmer 4 is the swimmer that is out of the pool for three consecutive time slots. So if Swimmers 1 and 2 are underwater for a different number of time slots, which is what D4 tells us, Swimmer 4 has to be the swimmer out of the pool for three consecutive time slots. This means A4 and C4 are out of the pool.

Step 7: C2 must be underwater to fulfill A5’s clue. D2 must be in the pool because of B4’s clue. C2’s clue says, ‘Swimmers 1 and 2 did the same thing at the same time as many times as Swimmers 2 and 3 did the same thing at the same time.’ Without knowing F2, Swimmers 2 and 3 are doing the same thing at three times. We know that B1 and D1 are in the pool and underwater, we just don’t know which one’s which. If B1 is in the pool and D1 is underwater, then Swimmers 1 and 2 are doing the same thing at the same time once. That wouldn’t fulfill C2’s clue so B1 must be underwater and D1 must be in the pool. D1’s clue tells us that no swimmer finished in the pool. This means that F2 cannot be in the pool. F2 also cannot be underwater so F2 myst be out of the pool.