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Pattern 15 and Pattern 30 Puzzles

Today I’m sharing two mathematical puzzles with you that Ivan Moscovich calls Pattern 15 and Pattern 30.

Earlier this school year, I browsed a bunch of puzzle books looking for puzzles to post in my classroom that didn’t involve manipulating pieces. This was weird for me because I was intentionally trying to avoid the exact puzzles that I most love to use with students in math class. Pandemics make us do weird things…

Puzzle of the Week Poster.

This search for “No Touching” puzzles led me to Ivan Moscovich’s Big Book of Brain Games : 1000 Playthinks of Art, Mathematics & Science. His Pattern 15 Puzzle caught my eye.

The puzzle reads: Five different whole numbers add up to 15. Multiply those same five numbers together, and the result is 120. What are those five numbers?

Pattern 15 Puzzle from Ivan Moscovich.

I eagerly started typing up this puzzle. Before I printed it, I decided I should probably try to solve the puzzle myself. I was quickly able to come up with an answer. This didn’t seem like much of a puzzle at all. I reread the original puzzle to make sure I hadn’t made a mistake. I even checked my answer with the answer provided in the book.

Difficulty Level of Playthink 14 Puzzle.

I’m confused because the book ranks this problem as having a difficulty of 7/10. I don’t exactly know what I am missing. I usually find Ivan Moscovich’s puzzles to be on the challenging side.

As a result of this confusion, I ended up not using this puzzle with my students. I ran across the puzzle yesterday while I was cleaning up the 1270 files that had been living on my desktop since the school year started. I have a bad habit of saving everything to my desktop thinking that I will sort it later. In cleaning up my desktop yesterday, I ran across this file and decided I needed to do something with it. I either needed to share the puzzle or delete it and pretend that I never came across it.

I took a look back at the puzzle book and realized that I don’t think that Pattern 15 is meant to be a stand-alone puzzle. Directly after Pattern 15, Ivan Moscovich challenges readers with Pattern 30. I think the Pattern 30 puzzle is a much more interesting puzzle.

Younger students may be challenged sufficiently with just the Pattern 15 puzzle.

The Pattern 30 puzzle also features five whole numbers which add up to 30. This time, however, the numbers are stated to be single-digit whole numbers. In addition, two of the numbers are provided.

Pattern 30 Puzzle from Ivan Moscovich.

Five different single-digit whole numbers add up to 30. Multiply those same five numbers together, and the result is 2520. What are those five numbers? Two of the numbers (1 and 8) have already been provided.

Puzzle Solutions

I intentionally do not make answers to the printable math puzzles I share on my blog available online because I strive to provide learning experiences for my students that are non-google-able. I would like other teachers to be able to use these puzzles in their classrooms as well without the solutions being easily found on the Internet.

However, I do recognize that us teachers are busy people and sometimes need to quickly reference an answer key to see if a student has solved a puzzle correctly or to see if they have interpreted the instructions properly.

If you are a teacher who is using these puzzles in your classroom, please send me an email at with information about what you teach and where you teach. I will be happy to forward an answer key to you.