It All Adds Up

We've got your numbers, but it's up to you to figure out where to put them

Row, Row, Row Your Square

**1. [Not so easy]** A magic square is a square grid of positive whole numbers in which every row, every column, and both main diagonals add up to the same sum. Can you arrange the numbers 1 through 9 in a 3x3 grid to make a magic square? The middle number, 5, has already been filled in.

**2. [Not so easy]** Can you put a 1, 2, or 3 in each square of a 3x3 grid to make a magic square? Each number will appear in three squares.

**3. [Not so easy]** Try finding a 3x3 magic square in which the sum of the first number minus the second number plus the third number in every row, column, and main diagonal is the same.

**4. [Difficult]** Can you arrange nine different positive whole numbers in a 3x3 grid so that every row, every column, and both main diagonals multiply to give the same product? The product should be as small as possible. Hint: Use the result from problem 2.

Can You Digit?

**1. [Easy]** Using each of the digits 0 through 9 just once, find a two-digit number and a four-digit number that add up to another four-digit number as shown at right. There are several solutions; find the smallest one possible. To get you started, we've filled in the four digits in the thousands and hundreds places, and here's the reasoning: Because no digit may be used twice, there must be a carryover from the tens to the hundreds place and from the hundreds to the thousands place. In the smallest possible solution, a 1 and a 2 must be in the thousands place. To get the carry-over into the thousands place, the two digits in the hundreds place must be 9 and 0. Can you complete the rest of the equation using each of the six remaining digits only once?

**2. [Not so easy]** Now find the solution with the largest possible total. (Bet you saw this coming!)

**3. [Not so easy]** Using each of the digits 0 through 9 just once, what are both the smallest and largest solutions for two three-digit numbers that add up to a four-digit number?

**4. [Easy]** Again, using each of the 10 digits just once, find a solution for eight single-digit numbers that add up to a two-digit number.

**5. [Difficult]** What correct equations can you assemble with the digits 0 through 9, a multiplication sign, and an equal sign? Can you find the solutions with the smallest and largest products? Hint: Neither of the smaller products can end in 0 or 1.

Factor Fiction

**1. [Easy]** 100 can be factored into two numbers, 4 and 25, neither of which contains a zero. Can you factor 1,000 into two numbers, neither of which contains a zero? How about 10,000?

**2. [Not so easy]** What is the smallest power of 10 that cannot be factored into exactly two numbers, neither of which contains a zero? Hint: You'll need a calculator for this one.

**3. [Very difficult]** What is the largest power of 10 that can be factored into exactly two numbers, neither of which contains a zero? Hint: This time, you should try a computer.

**Solution** Want to see the

solution to this puzzle?

Got new solutions for the puzzle? Want to see other people's solutions? Talk to the puzzle master in his discussion forum at

www.scottkim.com.

© Copyright 2001 The Walt Disney