DAY 196

THE CLEVER KING
20 artisans worked for a king making various pieces of gold jewelry. Each piece was supposed to weigh exactly 1 ounce. The king learned that one of the artisans was making his pieces consistently 1/8 oz. less and stealing the difference. The king was able to identify the culprit in only one weighing. How did he do it?

Answer:

The king took one piece of jewelry from the first workman, two from the second, three from the third, and so on. In total, the king had 1+2+3+4+5.......+20 or 210 pieces. If all were full weight, they would weigh 210 ounces. If the first artisan were cheating, the total weight would be short by 1/8 oz. If the second artisan were cheating, the total weight would be off by 1/4 oz. (2 x 1/8). If the sixth artisan were cheating, it would be off by 3/4 oz. (6 x 1/8), etc. Whatever number multiplied by 1/8 was equal to the shortage in the total weight would be the number of the cheating artisan.

DAY 197
The following addition problem uses each of the digits 1 - 10 once. What else is unusual about this problem?

35/70 + 148/296

Answer:

The sum is 1...........each term equals 1/2.