January 2017
Problem of the Month

Year Without Brackets
by Marek Penszko in GAMES

An old numerical problem is as follows:
1 2 3 4 5 6 7 8 9 = 100

Insert mathematical signs (+, -, ×, ÷) wherever you like between the digits to make the expression equal 100.   The digits must remain in the same order and if there is no sign between two or more digits, they combine to form a number.   There are many solutions without brackets or parentheses, for example
1 + 234 × 5 × 6 ÷ 78 + 9 = 100

Here is the current variation of this puzzle:
1 2 3 4 5 6 7 8 9 = 2017

Insert mathematical signs (+, -, ×, ÷) wherever you like between the digits to make the expression equal 2017.   The digits must remain in the same order and if there is no sign between two or more digits, they combine to form a number.   You must use the correct order of operations and you must not use any brackets or parentheses!

Solution to the Problem:

There are twin solutions with only five signs:
12 + 345 x 6 + 7 - 8 x 9 = 2017
12 + 345 x 6 - 7 x 8 - 9 = 2017

However, James Alarie sent in six solutions that work:

12 + 345 * 6 + 7 - 8 * 9 = 2017
12 + 345 * 6 - 7 * 8 - 9 = 2017
1 + 2 * 34 * 5 * 6 - 7 - 8 - 9 = 2017
-1 + 2345 - 6 * 7 * 8 + 9 = 2017
-1 * 2 + 3 + 4 * 567 * 8 / 9 = 2017
-1 * 2 + 3 / 4 * 5 * 67 * 8 + 9 = 2017

And then James followed that up with the following email:

You knew I couldn't leave this one alone, so I reversed the digits
(987654321) to get another answer:

98 * 76 - 5432 + 1 = 2017

If you'll allow a zero at the end (at the beginning makes no sense.),
I get twenty-one more:

1234 + 56 + 7 + 8 * 90 = 2017
12 + 345 * 6 + 7 - 8 * 9 + 0 = 2017
12 + 345 * 6 + 7 - 8 * 9 - 0 = 2017
12 + 345 * 6 - 7 * 8 - 9 + 0 = 2017
12 + 345 * 6 - 7 * 8 - 9 - 0 = 2017
1 + 2 + 345 * 6 - 7 * 8 + 9 * 0 = 2017
1 + 2 + 345 * 6 - 7 * 8 - 9 * 0 = 2017
1 + 2 * 34 * 5 * 6 - 7 - 8 - 9 + 0 = 2017
1 + 2 * 34 * 5 * 6 - 7 - 8 - 9 - 0 = 2017
1 - 234 + 5 * 6 * 78 - 90 = 2017
-1 + 2345 - 6 * 7 * 8 + 9 + 0 = 2017
-1 + 2345 - 6 * 7 * 8 + 9 - 0 = 2017
-1 + 2345 * 6 / 7 + 8 + 9 * 0 = 2017
-1 + 2345 * 6 / 7 + 8 - 9 * 0 = 2017
-1 + 234 * 5 - 6 * 7 + 890 = 2017
-1 + 2 / 3 * 45 * 67 + 8 + 9 * 0 = 2017
-1 + 2 / 3 * 45 * 67 + 8 - 9 * 0 = 2017
-1 * 2 + 3 + 4 * 567 * 8 / 9 + 0 = 2017
-1 * 2 + 3 + 4 * 567 * 8 / 9 - 0 = 2017
-1 * 2 + 3 / 4 * 5 * 67 * 8 + 9 + 0 = 2017
-1 * 2 + 3 / 4 * 5 * 67 * 8 + 9 - 0 = 2017

but only five more for the reverse:

98 * 76 - 5432 + 1 + 0 = 2017
98 * 76 - 5432 + 1 - 0 = 2017
9 + 8 * 76 + 5 * 4 / 3 * 210 = 2017
-9 + 8 * 7 + 654 * 3 - 2 + 10 = 2017
-9 * 8 * 7 + 6 - 5 + 4 * 3 * 210 = 2017

Correctly solved by:

1. James Alarie (Extra credit for finding 6 solutions)	Flint, Michigan
2. Hunter Gross	Mountain View High School, Mountain View, Wyoming
3. Wyatt Gross	Mountain View High School, Mountain View, Wyoming

Send any comments or questions to: David Pleacher