b. Salt it. Another strategy is to start with a word or phrase that is easy to r

Question

b. Salt it. Another strategy is to start with a word or phrase that is easy

to remember and then add some random changes to it. Bob starts with

Superman and then applies one modication to it where a modication

consists of inserting a number at some position. This process can produce

a string like Super5man.

b1. How many dierent strings can Bob create starting with Superman?

Suppose Bob wants to apply two modications to produce a string like

9Super5man or a string like Super95man. We want to determine the dif-

ferent strings Bob can create. He does this in two steps:

Step 1. Choose the rst number (say 5) and insert it in Superman. (It

produces Super5man, etc.)

Step 2. Choose the second number (say 9) and insert it in the string

obtained after Step 1. (If the string from step 1 was Super5man, then the

result can be 9Super5man or Super95man, etc.)

b2. To determine the number of dierent strings Bob can create, we can

just apply the Product Rule (Handout 8, page 3). Explain why the product

rule will result in overcounting. In particular, what strings will be counted

more than once?

b3. How would you solve the problem? Explain why you think it is correct.

Explanation / Answer

I think in the first step the possible number of posiiton where you can enter first number is 9. And then when you add second number there become 10 possible spaces where you can enter the second number. So the total number of strings which are possible are 9*10=90.

For first part you mentioned Product rule(Handout 8page 3), you should have uploaded it here for me to check. Or if you understand the logic you can check why it is leading to overcounting.

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