Past Microprocessor Question
There are 3 questions on this exam. You have 2 hours to complete it. Please do your own work.
1. The number 124 has the property that it is the smallest number whose first three multiples contain the digit 2. Observe that
124*1 = 124, 124*2 = 248, 124*3 = 372 and that 124, 248 and 372 each contain the digit 2. It is possible to generalize this property to be the smallest number whose first n multiples each contain the digit 2. Write a function named smallest(n) that returns the smallest number whose first n multiples contain the digit 2. Hint: use modulo base 10 arithmetic to examine digits.
Its signature is int smallest(int n)
You may assume that such a number is computable on a 32 bit machine, i.e, you do not have to detect integer overflow in your answer.
Examples
|If n is |return |because |
|4 |624 |because the first four multiples of 624 are 624, 1248, 1872, 2496 and they all contain the |
| | |digit 2. Furthermore 624 is the smallest number whose first four multiples contain the digit 2. |
|5 |624 |because the first five multiples of 624 are 624, 1248, 1872, 2496, 3120. Note that 624 is also |
| | |the smallest number whose first 4 multiples contain the digit 2. |
|6 |642 |because the first five multiples of 642 are 642, 1284, 1926, 2568, 3210, 3852 |
|7 |4062 |because the first five multiples of 4062 are 4062, 8124, 12186, 16248, 20310, 24372, 28434. |
| | |Note that it is okay for one of the multiples to contain the digit 2 more than once (e.g., 24372). |
2. Define a cluster in an integer array to be a maximum
1. The number 124 has the property that it is the smallest number whose first three multiples contain the digit 2. Observe that
124*1 = 124, 124*2 = 248, 124*3 = 372 and that 124, 248 and 372 each contain the digit 2. It is possible to generalize this property to be the smallest number whose first n multiples each contain the digit 2. Write a function named smallest(n) that returns the smallest number whose first n multiples contain the digit 2. Hint: use modulo base 10 arithmetic to examine digits.
Its signature is int smallest(int n)
You may assume that such a number is computable on a 32 bit machine, i.e, you do not have to detect integer overflow in your answer.
Examples
|If n is |return |because |
|4 |624 |because the first four multiples of 624 are 624, 1248, 1872, 2496 and they all contain the |
| | |digit 2. Furthermore 624 is the smallest number whose first four multiples contain the digit 2. |
|5 |624 |because the first five multiples of 624 are 624, 1248, 1872, 2496, 3120. Note that 624 is also |
| | |the smallest number whose first 4 multiples contain the digit 2. |
|6 |642 |because the first five multiples of 642 are 642, 1284, 1926, 2568, 3210, 3852 |
|7 |4062 |because the first five multiples of 4062 are 4062, 8124, 12186, 16248, 20310, 24372, 28434. |
| | |Note that it is okay for one of the multiples to contain the digit 2 more than once (e.g., 24372). |
2. Define a cluster in an integer array to be a maximum