One of the blogs I follow is Find The Factors. It’s very different from this one. For a start, it’s frighteningly efficient, and appears on a daily basis – not like this one, which happens now and again when I get around to it.
Iva Sallay gives us a new puzzle every day, where you’re given a few entries in a multiplication square and have to figure out the multipliers heading the columns and rows. So clearly we’re in an area highlighting multiplication facts – in the puzzle below the 42 in the top row has to be the product of 6 and 7 – but we can’t immediately do anything with this because we don’t know if it the 42 comes from 6×7 or 7×6. And the 20 will offer more problems, since we’ll have to discover whether it comes from the product of 2 and 10, or 4 and 5; even then, we must decide on the orientation.
A Find The Factors puzzle will be full of challenges like this, and the beauty of the blog is that they’re graded from level 1 all the way to the most challenging level 6. The puzzle below is level 4:
This puzzle is number 177, and you’ll usually get some facts about the puzzle number – its factorisation, and in this case, you’re also given a magic square made up of prime numbers; the magic total is 177.
The obvious comparison is to Sudoku puzzles. I rarely do Sudoku; I usually find I get so far and then have no option other than guessing between several possibilities until I find the right one. Just occasionally I’ve had to do this with Find The Factors, but generally speaking even at level 6 I can eventually reason the whole thing out. Mind you, sometimes I have to work hard, but that’s surely the whole idea!
I’ve shown one of Iva’s 1-12 puzzles, but she also gives 1-10 puzzles as well, and you can have a week’s worth of puzzles to download in Excel format.
You can find Iva’s blog at http://findthefactors.wordpress.com
I do the puzzles for my own enjoyment, but my pupils would find them daunting and indeed too time-consuming. However, the basic idea is one I’m happy to challenge them with, so I may offer them a 4×4 square constructed on the same theme. Once they’d tackled one of those, we’re likely to use the interactive version on the NRICH website (http://nrich.maths.org/7382) where you can find a variety of challenges all based on the same starting point).