Ambiguous Times

Theorem
Let $t$ be a time of day in $12$-hour clock form.

The following times of day are ambiguous:


 * {| border="1"

! align="center" style = "padding: 2px 10px" | Ambiguous Time ! align="center" style = "padding: 2px 10px" | Corresponding Time
 * align="center" style = "padding: 2px 10px" | $12 : 05 \tfrac 5 {143}$
 * align="center" style = "padding: 2px 10px" | $01 : 00 \tfrac {60} {143}$
 * align="center" style = "padding: 2px 10px" | $12 : 10 \tfrac {10} {143}$
 * align="center" style = "padding: 2px 10px" | $02 : 00 \tfrac {120} {143}$
 * align="center" style = "padding: 2px 10px" | $12 : 15 \tfrac {15} {143}$
 * align="center" style = "padding: 2px 10px" | $03 : 01 \tfrac {37} {143}$
 * align="center" style = "padding: 2px 10px" | $12 : 20 \tfrac {20} {143}$
 * align="center" style = "padding: 2px 10px" | $04 : 01 \tfrac {97} {143}$
 * align="center" style = "padding: 2px 10px" | $12 : 25 \tfrac {25} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 02 \tfrac {14} {143}$
 * align="center" style = "padding: 2px 10px" | $12 : 30 \tfrac {30} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 02 \tfrac {74} {143}$
 * align="center" style = "padding: 2px 10px" | $12 : 35 \tfrac {35} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 02 \tfrac {134} {143}$
 * align="center" style = "padding: 2px 10px" | $12 : 40 \tfrac {40} {143}$
 * align="center" style = "padding: 2px 10px" | $08 : 03 \tfrac {51} {143}$
 * align="center" style = "padding: 2px 10px" | $12 : 45 \tfrac {45} {143}$
 * align="center" style = "padding: 2px 10px" | $09 : 03 \tfrac {111} {143}$
 * align="center" style = "padding: 2px 10px" | $12 : 50 \tfrac {50} {143}$
 * align="center" style = "padding: 2px 10px" | $10 : 04 \tfrac {28} {143}$
 * align="center" style = "padding: 2px 10px" | $12 : 55 \tfrac {55} {143}$
 * align="center" style = "padding: 2px 10px" | $11 : 04 \tfrac {88} {143}$
 * align="center" style = "padding: 2px 10px" | $01 : 00 \tfrac {60} {143}$
 * align="center" style = "padding: 2px 10px" | $12 : 05 \tfrac 5 {143}$
 * align="center" style = "padding: 2px 10px" | $01 : 05 \tfrac {65} {143}$
 * align="center" style = "padding: 2px 10px" | $01 : 05 \tfrac {65} {143}$
 * align="center" style = "padding: 2px 10px" | $01 : 10 \tfrac {70} {143}$
 * align="center" style = "padding: 2px 10px" | $02 : 05 \tfrac {125} {143}$
 * align="center" style = "padding: 2px 10px" | $01 : 15 \tfrac {75} {143}$
 * align="center" style = "padding: 2px 10px" | $03 : 06 \tfrac {42} {143}$
 * align="center" style = "padding: 2px 10px" | $01 : 20 \tfrac {80} {143}$
 * align="center" style = "padding: 2px 10px" | $04 : 06 \tfrac {102} {143}$
 * align="center" style = "padding: 2px 10px" | $01 : 25 \tfrac {85} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 07 \tfrac {19} {143}$
 * align="center" style = "padding: 2px 10px" | $01 : 30 \tfrac {90} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 07 \tfrac {79} {143}$
 * align="center" style = "padding: 2px 10px" | $01 : 35 \tfrac {95} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 07 \tfrac {139} {143}$
 * align="center" style = "padding: 2px 10px" | $01 : 40 \tfrac {100} {143}$
 * align="center" style = "padding: 2px 10px" | $08 : 08 \tfrac {56} {143}$
 * align="center" style = "padding: 2px 10px" | $01 : 45 \tfrac {105} {143}$
 * align="center" style = "padding: 2px 10px" | $09 : 08 \tfrac {116} {143}$
 * align="center" style = "padding: 2px 10px" | $01 : 50 \tfrac {110} {143}$
 * align="center" style = "padding: 2px 10px" | $10 : 09 \tfrac {33} {143}$
 * align="center" style = "padding: 2px 10px" | $01 : 55 \tfrac {115} {143}$
 * align="center" style = "padding: 2px 10px" | $11 : 09 \tfrac {93} {143}$
 * align="center" style = "padding: 2px 10px" | $02 : 00 \tfrac {120} {143}$
 * align="center" style = "padding: 2px 10px" | $12 : 10 \tfrac {10} {143}$
 * align="center" style = "padding: 2px 10px" | $02 : 05 \tfrac {125} {143}$
 * align="center" style = "padding: 2px 10px" | $01 : 10 \tfrac {70} {143}$
 * align="center" style = "padding: 2px 10px" | $02 : 10 \tfrac {130} {143}$
 * align="center" style = "padding: 2px 10px" | $02 : 10 \tfrac {130} {143}$
 * align="center" style = "padding: 2px 10px" | $02 : 15 \tfrac {135} {143}$
 * align="center" style = "padding: 2px 10px" | $03 : 11 \tfrac {47} {143}$
 * align="center" style = "padding: 2px 10px" | $02 : 20 \tfrac {140} {143}$
 * align="center" style = "padding: 2px 10px" | $04 : 11 \tfrac {107} {143}$
 * align="center" style = "padding: 2px 10px" | $02 : 26 \tfrac 2 {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 12 \tfrac {24} {143}$
 * align="center" style = "padding: 2px 10px" | $02 : 31 \tfrac 7 {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 12 \tfrac {84} {143}$
 * align="center" style = "padding: 2px 10px" | $02 : 36 \tfrac {12} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 13 \tfrac 1 {143}$
 * align="center" style = "padding: 2px 10px" | $02 : 41 \tfrac {17} {143}$
 * align="center" style = "padding: 2px 10px" | $08 : 13 \tfrac {61} {143}$
 * align="center" style = "padding: 2px 10px" | $02 : 46 \tfrac {22} {143}$
 * align="center" style = "padding: 2px 10px" | $09 : 13 \tfrac {121} {143}$
 * align="center" style = "padding: 2px 10px" | $02 : 51 \tfrac {27} {143}$
 * align="center" style = "padding: 2px 10px" | $10 : 14 \tfrac {38} {143}$
 * align="center" style = "padding: 2px 10px" | $02 : 56 \tfrac {32} {143}$
 * align="center" style = "padding: 2px 10px" | $11 : 14 \tfrac {98} {143}$
 * align="center" style = "padding: 2px 10px" | $03 : 01 \tfrac {37} {143}$
 * align="center" style = "padding: 2px 10px" | $12 : 15 \tfrac {15} {143}$
 * align="center" style = "padding: 2px 10px" | $03 : 06 \tfrac {42} {143}$
 * align="center" style = "padding: 2px 10px" | $01 : 15 \tfrac {75} {143}$
 * align="center" style = "padding: 2px 10px" | $03 : 11 \tfrac {47} {143}$
 * align="center" style = "padding: 2px 10px" | $02 : 15 \tfrac {135} {143}$
 * align="center" style = "padding: 2px 10px" | $03 : 16 \tfrac {52} {143}$
 * align="center" style = "padding: 2px 10px" | $03 : 16 \tfrac {52} {143}$
 * align="center" style = "padding: 2px 10px" | $03 : 21 \tfrac {57} {143}$
 * align="center" style = "padding: 2px 10px" | $04 : 16 \tfrac {112} {143}$
 * align="center" style = "padding: 2px 10px" | $03 : 26 \tfrac {62} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 17 \tfrac {29} {143}$
 * align="center" style = "padding: 2px 10px" | $03 : 31 \tfrac {67} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 17 \tfrac {89} {143}$
 * align="center" style = "padding: 2px 10px" | $03 : 36 \tfrac {72} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 18 \tfrac 6 {143}$
 * align="center" style = "padding: 2px 10px" | $03 : 41 \tfrac {77} {143}$
 * align="center" style = "padding: 2px 10px" | $08 : 18 \tfrac {66} {143}$
 * align="center" style = "padding: 2px 10px" | $03 : 46 \tfrac {82} {143}$
 * align="center" style = "padding: 2px 10px" | $09 : 18 \tfrac {126} {143}$
 * align="center" style = "padding: 2px 10px" | $03 : 51 \tfrac {87} {143}$
 * align="center" style = "padding: 2px 10px" | $10 : 19 \tfrac {43} {143}$
 * align="center" style = "padding: 2px 10px" | $03 : 56 \tfrac {92} {143}$
 * align="center" style = "padding: 2px 10px" | $11 : 19 \tfrac {103} {143}$
 * align="center" style = "padding: 2px 10px" | $04 : 01 \tfrac {97} {143}$
 * align="center" style = "padding: 2px 10px" | $12 : 20 \tfrac {20} {143}$
 * align="center" style = "padding: 2px 10px" | $04 : 06 \tfrac {102} {143}$
 * align="center" style = "padding: 2px 10px" | $01 : 20 \tfrac {80} {143}$
 * align="center" style = "padding: 2px 10px" | $04 : 11 \tfrac {107} {143}$
 * align="center" style = "padding: 2px 10px" | $02 : 20 \tfrac {140} {143}$
 * align="center" style = "padding: 2px 10px" | $04 : 16 \tfrac {112} {143}$
 * align="center" style = "padding: 2px 10px" | $03 : 21 \tfrac {57} {143}$
 * align="center" style = "padding: 2px 10px" | $04 : 21 \tfrac {117} {143}$
 * align="center" style = "padding: 2px 10px" | $04 : 21 \tfrac {117} {143}$
 * align="center" style = "padding: 2px 10px" | $04 : 26 \tfrac {122} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 22 \tfrac {34} {143}$
 * align="center" style = "padding: 2px 10px" | $04 : 31 \tfrac {127} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 22 \tfrac {94} {143}$
 * align="center" style = "padding: 2px 10px" | $04 : 36 \tfrac {132} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 23 \tfrac {11} {143}$
 * align="center" style = "padding: 2px 10px" | $04 : 41 \tfrac {137} {143}$
 * align="center" style = "padding: 2px 10px" | $08 : 23 \tfrac {71} {143}$
 * align="center" style = "padding: 2px 10px" | $04 : 46 \tfrac {142} {143}$
 * align="center" style = "padding: 2px 10px" | $09 : 23 \tfrac {131} {143}$
 * align="center" style = "padding: 2px 10px" | $04 : 52 \tfrac 4 {143}$
 * align="center" style = "padding: 2px 10px" | $10 : 24 \tfrac {48} {143}$
 * align="center" style = "padding: 2px 10px" | $04 : 57 \tfrac 9 {143}$
 * align="center" style = "padding: 2px 10px" | $11 : 24 \tfrac {108} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 02 \tfrac {14} {143}$
 * align="center" style = "padding: 2px 10px" | $12 : 25 \tfrac {25} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 07 \tfrac {19} {143}$
 * align="center" style = "padding: 2px 10px" | $01 : 25 \tfrac {85} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 12 \tfrac {24} {143}$
 * align="center" style = "padding: 2px 10px" | $02 : 26 \tfrac 2 {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 17 \tfrac {29} {143}$
 * align="center" style = "padding: 2px 10px" | $03 : 26 \tfrac {62} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 22 \tfrac {34} {143}$
 * align="center" style = "padding: 2px 10px" | $04 : 26 \tfrac {122} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 27 \tfrac {39} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 27 \tfrac {39} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 32 \tfrac {44} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 27 \tfrac {99} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 37 \tfrac {49} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 28 \tfrac {16} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 42 \tfrac {54} {143}$
 * align="center" style = "padding: 2px 10px" | $08 : 28 \tfrac {76} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 47 \tfrac {59} {143}$
 * align="center" style = "padding: 2px 10px" | $09 : 28 \tfrac {136} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 52 \tfrac {64} {143}$
 * align="center" style = "padding: 2px 10px" | $10 : 29 \tfrac {53} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 57 \tfrac {69} {143}$
 * align="center" style = "padding: 2px 10px" | $11 : 29 \tfrac {113} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 02 \tfrac {74} {143}$
 * align="center" style = "padding: 2px 10px" | $12 : 30 \tfrac {30} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 07 \tfrac {79} {143}$
 * align="center" style = "padding: 2px 10px" | $01 : 30 \tfrac {90} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 12 \tfrac {84} {143}$
 * align="center" style = "padding: 2px 10px" | $02 : 31 \tfrac 7 {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 17 \tfrac {89} {143}$
 * align="center" style = "padding: 2px 10px" | $03 : 31 \tfrac {67} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 22 \tfrac {94} {143}$
 * align="center" style = "padding: 2px 10px" | $04 : 31 \tfrac {127} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 27 \tfrac {99} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 32 \tfrac {44} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 32 \tfrac {104} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 32 \tfrac {104} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 37 \tfrac {109} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 33 \tfrac {21} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 42 \tfrac {114} {143}$
 * align="center" style = "padding: 2px 10px" | $08 : 33 \tfrac {81} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 47 \tfrac {119} {143}$
 * align="center" style = "padding: 2px 10px" | $09 : 33 \tfrac {141} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 52 \tfrac {124} {143}$
 * align="center" style = "padding: 2px 10px" | $10 : 34 \tfrac {58} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 57 \tfrac {129} {143}$
 * align="center" style = "padding: 2px 10px" | $11 : 34 \tfrac {118} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 02 \tfrac {134} {143}$
 * align="center" style = "padding: 2px 10px" | $12 : 35 \tfrac {35} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 07 \tfrac {139} {143}$
 * align="center" style = "padding: 2px 10px" | $01 : 35 \tfrac {95} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 13 \tfrac 1 {143}$
 * align="center" style = "padding: 2px 10px" | $02 : 36 \tfrac {12} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 18 \tfrac 6 {143}$
 * align="center" style = "padding: 2px 10px" | $03 : 36 \tfrac {72} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 23 \tfrac {11} {143}$
 * align="center" style = "padding: 2px 10px" | $04 : 36 \tfrac {132} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 28 \tfrac {16} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 37 \tfrac {49} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 33 \tfrac {21} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 37 \tfrac {109} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 38 \tfrac {26} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 38 \tfrac {26} {143}$
 * }
 * align="center" style = "padding: 2px 10px" | $05 : 12 \tfrac {24} {143}$
 * align="center" style = "padding: 2px 10px" | $02 : 26 \tfrac 2 {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 17 \tfrac {29} {143}$
 * align="center" style = "padding: 2px 10px" | $03 : 26 \tfrac {62} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 22 \tfrac {34} {143}$
 * align="center" style = "padding: 2px 10px" | $04 : 26 \tfrac {122} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 27 \tfrac {39} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 27 \tfrac {39} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 32 \tfrac {44} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 27 \tfrac {99} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 37 \tfrac {49} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 28 \tfrac {16} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 42 \tfrac {54} {143}$
 * align="center" style = "padding: 2px 10px" | $08 : 28 \tfrac {76} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 47 \tfrac {59} {143}$
 * align="center" style = "padding: 2px 10px" | $09 : 28 \tfrac {136} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 52 \tfrac {64} {143}$
 * align="center" style = "padding: 2px 10px" | $10 : 29 \tfrac {53} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 57 \tfrac {69} {143}$
 * align="center" style = "padding: 2px 10px" | $11 : 29 \tfrac {113} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 02 \tfrac {74} {143}$
 * align="center" style = "padding: 2px 10px" | $12 : 30 \tfrac {30} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 07 \tfrac {79} {143}$
 * align="center" style = "padding: 2px 10px" | $01 : 30 \tfrac {90} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 12 \tfrac {84} {143}$
 * align="center" style = "padding: 2px 10px" | $02 : 31 \tfrac 7 {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 17 \tfrac {89} {143}$
 * align="center" style = "padding: 2px 10px" | $03 : 31 \tfrac {67} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 22 \tfrac {94} {143}$
 * align="center" style = "padding: 2px 10px" | $04 : 31 \tfrac {127} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 27 \tfrac {99} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 32 \tfrac {44} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 32 \tfrac {104} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 32 \tfrac {104} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 37 \tfrac {109} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 33 \tfrac {21} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 42 \tfrac {114} {143}$
 * align="center" style = "padding: 2px 10px" | $08 : 33 \tfrac {81} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 47 \tfrac {119} {143}$
 * align="center" style = "padding: 2px 10px" | $09 : 33 \tfrac {141} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 52 \tfrac {124} {143}$
 * align="center" style = "padding: 2px 10px" | $10 : 34 \tfrac {58} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 57 \tfrac {129} {143}$
 * align="center" style = "padding: 2px 10px" | $11 : 34 \tfrac {118} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 02 \tfrac {134} {143}$
 * align="center" style = "padding: 2px 10px" | $12 : 35 \tfrac {35} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 07 \tfrac {139} {143}$
 * align="center" style = "padding: 2px 10px" | $01 : 35 \tfrac {95} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 13 \tfrac 1 {143}$
 * align="center" style = "padding: 2px 10px" | $02 : 36 \tfrac {12} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 18 \tfrac 6 {143}$
 * align="center" style = "padding: 2px 10px" | $03 : 36 \tfrac {72} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 23 \tfrac {11} {143}$
 * align="center" style = "padding: 2px 10px" | $04 : 36 \tfrac {132} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 28 \tfrac {16} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 37 \tfrac {49} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 33 \tfrac {21} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 37 \tfrac {109} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 38 \tfrac {26} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 38 \tfrac {26} {143}$
 * }
 * align="center" style = "padding: 2px 10px" | $06 : 52 \tfrac {124} {143}$
 * align="center" style = "padding: 2px 10px" | $10 : 34 \tfrac {58} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 57 \tfrac {129} {143}$
 * align="center" style = "padding: 2px 10px" | $11 : 34 \tfrac {118} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 02 \tfrac {134} {143}$
 * align="center" style = "padding: 2px 10px" | $12 : 35 \tfrac {35} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 07 \tfrac {139} {143}$
 * align="center" style = "padding: 2px 10px" | $01 : 35 \tfrac {95} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 13 \tfrac 1 {143}$
 * align="center" style = "padding: 2px 10px" | $02 : 36 \tfrac {12} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 18 \tfrac 6 {143}$
 * align="center" style = "padding: 2px 10px" | $03 : 36 \tfrac {72} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 23 \tfrac {11} {143}$
 * align="center" style = "padding: 2px 10px" | $04 : 36 \tfrac {132} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 28 \tfrac {16} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 37 \tfrac {49} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 33 \tfrac {21} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 37 \tfrac {109} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 38 \tfrac {26} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 38 \tfrac {26} {143}$
 * }
 * align="center" style = "padding: 2px 10px" | $07 : 28 \tfrac {16} {143}$
 * align="center" style = "padding: 2px 10px" | $05 : 37 \tfrac {49} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 33 \tfrac {21} {143}$
 * align="center" style = "padding: 2px 10px" | $06 : 37 \tfrac {109} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 38 \tfrac {26} {143}$
 * align="center" style = "padding: 2px 10px" | $07 : 38 \tfrac {26} {143}$
 * }
 * align="center" style = "padding: 2px 10px" | $07 : 38 \tfrac {26} {143}$
 * }

Proof
Let $T$ be an ambiguous time.

Let $T$ be specified in hours $h$ and minutes $m$, where:
 * $1 \le h \le 12$ is an integer
 * $0 \le m < 60$ is a real number

whether a.m. or p.m. is immaterial.

At this time $T$:


 * let $\theta \degrees$ be the angle made by the minute hand with respect to twelve o'clock


 * let $\phi \degrees$ be the angle made by the hour hand with respect to twelve o'clock.

$\theta$ and $\phi$ give a valid time indication by definition.

From Condition for Valid Time Indication:


 * $12 \phi \mod 360 = \theta$

By definition of ambiguous time, we have that if the hour hand and minute hand were reversed, the time of day indicated is also a valid time indication.

That is:
 * $12 \theta \mod 360 = \phi$

Hence:

It follows directly that $\theta = 12 \phi \mod 360$.

It remains to calculate $\dfrac {360 k} {143}$ and convert the number each time into a valid time indication:

and so forth:

These are the ambiguous times corresponding to the times of day between $12:00$ and $01:00$.

It remains to calculate:
 * $(1) \quad$ the angles made by the minute hand at these times


 * $(2) \quad$ work out the times of day corresponding to the hour hand at these angles.

Let us take the ambiguous time $12 : 05 \tfrac 5 {143}$.

The hour hand is at $\dfrac {360} {143} \degrees$ while the minute hand is at $\dfrac {12 \times 360} {143} \degrees = 30 \tfrac {30} {143} \degrees$.

Exchanging the hour hand and minute hand gives us a time soon after $1:00$ where the minute hand is at $\dfrac {360} {143} \degrees$.

From Speed of Minute Hand, the minute hand moves at $6 \degrees$ per minute.

This leads us to a time of $\dfrac {360} {6 \times 143}$ minutes after $1:00$, or $\dfrac {60} {143}$ minutes after $1:00$.

To check our arithmetic, we investigate the hour hand position at $01 : 00 \tfrac {60} {143}$

A time of $\tfrac {60} {143}$ past the hour corresponds to an angle of $\dfrac 1 2 \tfrac {60} {143} \degrees$, or $\tfrac {30} {143} \degrees$ past $30 \degrees$.

This agrees with our calculation of the position of the minute hand.

The remaining corresponding times are evaluated as multiples of this time.