"For Math Lovers" Combination Lock (1)?

Question

A combination lock has some identical cylindrical tumblers each with the digits from 0-9 inclusive printed on each of the cylinders. The cylinders are aligned on a common axis. Each cylinder can be spun so that only one digit is visible on each cylinder. The digits when read from left to right form an integer. However, for these problems, we will allow an integer to start with a 0, such as 0123. If the displayed number is the correct combination the lock can be opened. Use the clues to open each of the following locks.



The first lock has two cylinders.

The sum of the tens digit and ones digit is 9.

The tens digit is less than the ones digit.

The ones digit is a square number.

What is the two-digit number that opens this lock?

Answer 1

x=tens
y=ones
x+y=9
x y=1,4, or 9
so x=0 and y=9

Answer 2

Ooh, I love these!

OK, let x be the tens digit and y the ones digit. Then from the first clue you know that

x + y = 9

From the third clue, y is either 1,4 or 9.

From the second clue, x < y. The only way (given the three values for y above) that all three conditions can be true is if x = 0 and y=9.

So the combination is 09.

Answer 3

_ _ _ The tens and ones digit must be 1 and 8, 2 and 4, 4 and 2, or 8 and 1 respectively. Since the tens digit is the sum of the hundreds digit and the ones digit, it must be greater than the ones digit. So we have _ 4 2 or _ 8 1 Then the hundreds digit is the positive difference of the ones digit and the tens digit. So we have 2 4 2 or 7 8 1 I presume "The three digit number is greater than 44." was a typo, and 44 should be something like 244 instead, so I'd say the answer is 781.

Answer 4

This lock's combination is "0-9"

0+9=9

0<9

9/3=3

Answer 5

0 and 9

0+9=9
0 is less then 9
the square root of nine is 3

Answer 6

81