Question

Fiona’s Number:

Answer 1

Answer:

289-743-1560

Step-by-step explanation:

im a genius (true it took me half an hour but i did it)

Answer 2

Answer:

He should dial 289-743-1560

Step-by-step explanation:

The first three digits:  "My first three digits are the square of an integer less than twenty"

Step 1:   We can get the first three by looking at the squares of the integers from 1 to 19.  We need a three digit number, so starting with 10, since 10² = 100, we list the squares of the integers from 10 to 19

10² = 100

11² = 121

12² = 144

13² = 169

14² = 196

15² = 225

16² = 256

17² = 289

18² = 324

19² = 361

Step 2:  "The first three digits are in ascending order" and no digits can repeat, so we eliminate the answers above that don't satisfy both of these condintions.  This leaves just 3 choices:

13² = 169

16² = 256

17² = 289

*We will come back to this once we have more information.

The last 2 numbers: "the last two digits are multiples of sixty".  

The only 2 digit number that is a multiple of 60 is 60, so 6 and 0 are the last 2 digits.  This rules out two answers from Step 1 since no digits can repeat.  Only 289 works since 169 and 256 each have a 6 in them.  So now we know the first 3, and last 2 numbers!

                                     2 8 9 _ _ _ _ _ 6 0

The last 4 numbers: "the last 4 digits are multiples of sixty"

We want to find a 4 four digit number that has 60 as the last 2 digits.  Notice a pattern when you multiply 60 by certain digits...

60 x 1 = 60

60 x 2 = 120

...

60 x 6 = 360

60 x 11 = 660

60 x 16 = 960     (these all don't work since they are not 4 digits)

60 x 21 = 1260     (this is the first 4 digit result, but it doesn't work because

                              there is a '2' in it, and 2 has already been used as the

                               first digit of the number)

60 x 26 = 1560     (this number could work, so lets try it and see if we can

                               satisfy the rest of the statements)

Now our number is

  2 8 9 _ _ _ 1 5 6 0

The second three digits:  "The second three digits are in descending order"  and "The sum of the second three digits is 14"

If we assume that 1, 5, 6 and 0 are the last four digits, we know that 2, 8 and 9 are the first three digits, this leaves 3, 4 and 7 as the three remaining digits.  

3 + 4 + 7 = 14     so that condition is satisfied.   We just need to write then in descending order, so our final number is

289-743-1560