Yesterday’s Problem:
Three nickels and three dimes are distributed among three piggy banks such that each piggy bank holds two coins. One piggy bank has a label of 20 cents. One bank has a label of 15 cents. And, one bank has a label pf 10 cents.
There is a problem. Although each bank has a label showing how much money is supposed to be found in each piggy bank respectively, all three piggy banks are mislabeled.
Is it possible to determine how to correctly re-label the banks simply by shaking one of the banks until one of the coins drops out? If so, how could this be possible?
Answer:
If you shake one of the coins out of the bank labeled 15 cents, you can figure out how to correctly label all the banks.
Since you know that the bank is mislabeled, it cannot hold 15 cents- instead, the bank contains either two dimes or two nickels. The coin that drops out will tell you what the other coin is.
Say the answer is two dimes: that leaves you with three nickels and a dime between the two remaining piggy banks, one labeled 20 cents and one labeled 10 cents. Since the bank labeled 10 cents cannot have two nickels in it – because it is mislabeled – it must contain a nickel and a dime and the other bank must have the two nickels.
Today’s Problem:
At the chalkboard the teacher demonstrates the four factors of the number 6. That is to say, the whole numbers that can divide into 6 and leave no remainder. For the number six, the four factors are 1,2,3 and 6. (Remember, a number is always its own factor, as is 1.)
Between 1 and 100 there are five numbers that have exactly twelve factors. How quickly can you find all five?