快猫短视频

#153 Tightwad鈥檚 safe

Tom Tightwad keeps his money in a safe, the code for which is a 10-digit number that uses every digit between 0 and 9.

Fearful of forgetting the code, Tom wrote it on the front of the safe, but disguised it. He wrote the first five digits along the top of a 5脳5 grid, and the last five digits down the side. Then he multiplied each digit along the top by each digit down the side, filling the grid with 25 numbers. Finally, he erased his code number from the top and side so that only the grid remained.

Unfortunately, the clumsy fellow also erased most of the numbers in the grid. And of what remains, some digits are so hard to read that they have been replaced with an 鈥淴鈥� (for example, in the diagram, the code鈥檚 first digit multiplied by its eighth digit is now 鈥�20-something鈥�).

Can you crack the safe?

#152 Lightning strike

Solution

Call the time of the first strike T1. After that, the clock reverses, and 30 minutes later the clock is 1 hour behind real time. Another lightning strike now makes the clock reverse again, going forwards but 1 hour behind. Thirty minutes later (at T2), the third strike reverses the clock again. The times on the bedside clock and my watch coincide at 7 o鈥檆lock, so T2 must be 1.30am (when the bedside clock was an hour behind). T2 was two strikes (1 hour) after T1, so the first strike was at 12.30am.