# Arithmetic 6: Digit Recreations

In all the puzzles that follow, the allowed operations and symbols are plus, minus, times, divide, exponentiation, radical, factorial, and parenthesis, except where otherwise noted.

1. Find an expression that uses the nine digits 1, 2, 3, … 9 in this order and equals 100. The plus and minus signs are forbidden.

2. Find an expression that uses the nine digits 1, 2, 3, … 9 in this order and equals 99. The plus and minus signs are forbidden.

3. Find an expression that uses four eights and equals 100.

4. Find an expression that uses four threes and equals 100.

[Solutions on page 2]

# Arithmetic 5: A One-Minute Puzzle

The number 24678051 equals the sum of the eighth powers of its digits, $24678051$ = $2^8$ + $4^8$ + $6^8$ + $7^8$ + $8^8$ + $0^8$ + $5^8$ + $1^8$. Can you find at least one other multidigit integer that has this property?

[Solution on page 2]

# Arithmetic 4: Dominoes

Place eight domino tiles from a standard domino set as shown, so that they form both (a) a correct domino chain, i.e., touch by equal numbers only, and (b) a correct multiplication.

# Arithmetic 3

Place the numbers from 1 to 9 inside the circles and replace each black dot with one of the four basic arithmetic symbols (plus, minus, times, divide) so that the six expressions thus formed equal the numbers 5, 14, 16, 39, 65, and 67 in some order. Multiplication and division are carried out before addition and subtraction; in the case of two operations of the same priority, the leftmost one is executed first. All rows read from left to right, the first and last columns read from top to bottom, and the middle column reads from bottom to top.

[Solution on page 2]

# Arithmetic 2

Place the numbers from 1 to 12 inside the circles and one of the four basic arithmetic symbols (plus, minus, times, divide) inside each square so that all six statements thus formed (five identities and a congruence) are true. Multiplication and division are carried out before addition and subtraction; in the case of two operations of the same priority, the leftmost one is executed first. All rows read from left to right and all columns read from top to bottom.

# Arithmetic 1

Place the numbers from 1 to 11 inside the boxes so that the sums of the numbers along all straight lines and the circle are the same.