Question

Ivan and Adeline are in a classroom with a chalkboard. They are standing on different halves of the board, and on each half, the number is written. When Ivan's teacher gives a signal, Ivan multiplies the number on his side of the board by and writes the answer on the board, erasing the number he started with. Adeline does the same on each signal, except that she multiplies by . The teacher gives 10 signals in total. How many times (including the initial number) do Ivan and Adeline have the same number written on the board

Answer 1

6 times

Explanation:

Given

`Start=2`

`Ivan=-2` ---- i.e. multiplies by -2

`Adeline = 2` --- i.e. multiplies by 2

`n=10` --- signals

Required

Number of times they have the same number

First, we list out all results of Ivan calculations.

To calculate Ivan's list, we simply multiply the current term by -2.

The 10 signals together with the first term, means there will be 11 terms in total

So, we have:

`Ivan = \{2,-4,8,-16,32,-64,128,-256,512,-1024,2048\}`

Next, list Adeline's

`Adeline = \{2,4,8,16,32,64,128,256,512,1024,2048\}`

Compare the elements of the two lists, we have:

`Common= \{2,8,32,128,512,2048\}`

Hence, they have the same number 6 times.