memory hieracrcy

  

1) You have been assigned the task of computing the sum of 1,000 four-digit numbers as rapidly as possible. You hold in your hands a stack of 1,000 index cards, each containing a single number, and you are in charge of 1,000 expert accountants, each with a calculator. You may choose to use the services of any number of accountants. The accountants are sitting at desks in a cavernous room. The desks are organized in to 25 rows and 40 columns. Each accountant is able to pass cards to the four accountants nearest him – in front, in back, to his left, and to his right.

a. Describe a fast method of distributing cards to accounts.

b. Describe a fast method of accumulating subtotals generated by active accountants into a grand total.

c. Explain why 1,000 accountants cannot perform the task 1,000 times faster than one accountant.

d. Find another way to arrange the desks of the accountants to reduce the time needed to distribute cards and collect subtotals. Describe the new desk arrangement, the new communication pattern, and the new estimate for time spent distributing cards and accumulating subtotals.