The keypad on my friend's microwave is broken: only one of the number keys (the N key) works. He found a workaround that allows him to cook for exactly 2 minutes, which is perfect for rewarming his giant cup of coffee. He does this by entering NN seconds, then start. He cooks for a period of time and then hits the pause button followed by N and start. (On his microwave, entering 99 would be the same as entering 139, since the 3rd number from the right is minutes)

For example, if N were "1", he could enter 11, cook until the display reads 6, pause, enter 1 (the display then reads 61), and cook for a total of 66 seconds. He also brags that using the same N key as above, but by pausing at a different time, he can cook for another whole number of minutes (other than 2).

Which number key is working on his microwave?

(In reply to And the winning number is... by Bob Smith)

Other times available with only the 7 key working, and using a single or double press initially, and then a single press are given in the following table. The columns are the initial entry, the timed interval, the delay before pausing and the reading at the pause.

 7  0:14     7  0
 7  0:23     6  1
 7  0:32     5  2
 7  0:41     4  3
 7  0:50     3  4
 7  0:59     2  5
 7  1: 8     1  6
77  1:24    77  0
77  1:33    76  1
77  1:42    75  2
77  1:51    74  3
77  2: 0    73  4
77  2: 9    72  5
77  2:14    67 10
77  2:18    71  6
77  2:23    66 11
77  2:27    70  7
77  2:32    65 12
77  2:36    69  8
77  2:41    64 13
77  2:45    68  9
77  2:50    63 14
77  2:59    62 15
77  3: 4    57 20
77  3: 8    61 16
77  3:13    56 21
77  3:17    60 17
77  3:22    55 22
77  3:26    59 18
77  3:31    54 23
77  3:35    58 19
77  3:40    53 24
77  3:49    52 25
77  3:54    47 30
77  3:58    51 26
77  4: 3    46 31
77  4: 7    50 27
77  4:12    45 32
77  4:16    49 28
77  4:21    44 33
77  4:25    48 29
77  4:30    43 34
77  4:39    42 35
77  4:44    37 40
77  4:48    41 36
77  4:53    36 41
77  4:57    40 37
77  5: 2    35 42
77  5: 6    39 38
77  5:11    34 43
77  5:15    38 39
77  5:20    33 44
77  5:29    32 45
77  5:34    27 50
77  5:38    31 46
77  5:43    26 51
77  5:47    30 47
77  5:52    25 52
77  5:56    29 48
77  6: 1    24 53
77  6: 5    28 49
77  6:10    23 54
77  6:19    22 55
77  6:24    17 60
77  6:28    21 56
77  6:33    16 61
77  6:37    20 57
77  6:42    15 62
77  6:46    19 58
77  6:51    14 63
77  6:55    18 59
77  7: 0    13 64
77  7: 9    12 65
77  7:14     7 70
77  7:18    11 66
77  7:23     6 71
77  7:27    10 67
77  7:32     5 72
77  7:36     9 68
77  7:41     4 73
77  7:45     8 69
77  7:50     3 74
77  7:59     2 75
77  8: 8     1 76

Posted by Charlie on 2005-11-08 11:29:30