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?

FOR n = 1 TO 9
 had2 = 0: hadOther = 0
 FOR delay = 1 TO 11 * n
  remain = 11 * n - delay
  m = remain \ 10: s = 10 * (remain MOD 10) + n
  tot = delay + m * 60 + s
  IF tot = 120 THEN
   had2 = 1
   delay2 = delay
  ELSEIF tot MOD 60 = 0 THEN
   hadOther = 1: otherMin = tot / 60
   delayHold = delay
  END IF
 NEXT
 IF had2 AND hadOther THEN
  PRINT n, delayHold; otherMin, delay2; 2
 END IF
NEXT

finds the 7 key with a delay of 13 seconds gives 7 minutes, and a delay of 73 seconds gives 2 minutes.

The solutions depend on the friend being able to pause, key the button and start again in negligible time.

Posted by Charlie on 2005-11-08 11:01:51