PROBLEM 1-8-7

My parents were still unpacking. It was my first day at the new school, and I was almost out the door when Mom shouted, “Phone home at lunchtime. We’ll want to know how the morning went.”

“But I don’t know the new phone number!”

“It’s easy,” Mom called, “just remember:

• the 1st, 2nd, and 3rd digits are all the same. Together they form a 3-digit number that is 70 less than the square of the product of the first two digits.
• The 4th digit is the greatest common factor of 28 and 35.
• The 5th digit is the cube root of 27.
• The 6th digit is the fourth prime number.
• Subtract -9 from -6. The difference if the 7th digit.”

What is the new phone number?

SOLUTION 1-8-7

The 1st, 2nd and 3rd digits are all 5’s because the product of the first two digits, 5 and 5, is 25 and 25 squared (25 x 25) is 625, and 625 minus 70 is 555.

The 4th digit is 7 because it is the greatest common factor of 28 and 35.

The 5th digit is 3 because 3 cubed is 27.

The 6th digit is 7 since it is the fourth prime number.

The 7th digit is 3 because -6 - -9 = 3.

The new phone number is 555-7373.