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
