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#152: At what time did a lightning strike change the clock?

At my bedside, I have a traditional-style electric clock wired to the mains. It has a curious fault. Whenever there is a lightning strike on the village鈥檚 electricity substation, the power surge causes my clock to reverse direction.

When I went to bed last night, I could tell that a storm was brewing, but I managed to sleep through it. When I woke this morning, the clock said 7 o鈥檆lock, and a quick check of my wristwatch confirmed that this was indeed the correct time.

But I just heard on the local news that there had been three lightning strikes on the substation during the night with exactly 30 minutes between each strike.

At what time was the first lightning strike?

Solution next week

#151 Alien fingers

Solution

For the purposes of this solution, we will call the two-digit number in hexadecimal PQ. Because it is hexadecimal (base 16), in our notation, PQ stands for (P 脳 16) + Q, and this must equal the number in our usual base-10 decimal notation that we write as QP, which is (Q x 10) + P. That way, 16P + Q = 10Q + P, which simplifies to 15P = 9Q. That is, 5P = 3Q. The only digits that fit this are P = 3 and Q = 5.

So the number as it appeared on the alien spaceship was 35, which was hexadecimal for our 53, as (3 x 16) + 5 = 53.