# Statement Snap

*Statement Snap printable sheet - instructionsStatement Snap printable sheet - cards*

*You might like to take a look at the problem Satisfying Statements, as the game and the problem complement one another.***You'll need to know your number properties to win a game of Statement Snap... **

To play the game, you'll need to print and cut out this set of cards

This game works well for 2 to 4 players.**How to play**

Shuffle the cards, and place them face down on the table.

Turn over two cards so that all the players can see them.

The object of the game is to find a number that satisfies the statements on both cards.

For example, if the cards said "A multiple of 6" and "A factor of 90" you could pick the number 30.

After ten seconds, everyone declares a number that satisfies both cards, and then the next round begins by turning over the next two cards.**Scoring**

There are a few different scoring options for the game:

- Score a point if you find a number that satisfies both cards
- Score a point if you think of the highest number that satisfies both cards
- List as many numbers as you can that satisfy both cards, and then score a point for each one.
- List as many numbers as you can, and then score a point for each number on your list that doesn't appear on anybody else's list.

**Impossible pairs!**

Sometimes there might not be any numbers that satisfy both statements! If this happens, you can replace one of the cards with a new one.**A Final Challenge**

Once you have played the game a few times, click below to see a few questions to explore:

How many impossible pairs can you find?

Can you find a number that satisfies 3 cards? Or 4 cards? Or...?

After playing this game several times, we suggested that you might like to search for some impossible pairs of cards as well as numbers which satisfy three or even four cards.

We received a solution from Ariel, who sent in a list of several pairs of impossible cards.

Ariel suggested that the the 'Square number' and 'Prime number' cards are an impossible pair. Is she correct? You might find it helpful to think about some actual numbers to help to convince yourself about your answer. What do you notice about the factors of square numbers such as 25 and 49? What's different between them and the factors of prime numbers like 13 and 23?

She also suggested that 'Two less than a multiple of 10' and 'One more than a multiple of 5' were an impossible pair. Again, it might be helpful to think about some actual numbers to help you to decide whether she is correct. What do you notice about a list of numbers which are two less than a multiple 10? Now consider listing some numbers which are one more than a multiple of 5. When you compare your two lists, what do you notice?

Here's the rest of Ariel's list of impossible pairs:

'The product of two primes' and 'A prime number.'

'The product of two primes' and 'A square number'

'Multiple of 3 but not multiple of 9' and 'Digits sum to 9'

'Odd number' and 'Even number that is not a multiple of 4'

'Odd number' and 'Two less than a multiple of 10'

'A multiple of 7' and 'A factor of 24'

'A multiple of 7' and 'A Factor of 60'

Are they all impossible pairs? Can you explain your reasoning?

We also asked about any numbers which satisifed three or four cards. Ariel suggested the following examples:

9 satisfies 3 cards, which are a square number, digits sum to 9 and an odd number.

0 also satisfies 3 cards, which are one less than a square number, a square number and a multiple of 7. Since 0 also satisfies the requirements of a triangular number (but this is argued), you can say that it satisfies 4 cards too.

2 satisfies 4 cards, which are a prime number, an even number but not a multiple of 4, a factor of 24 and a factor of 60.

Ariel also explored whether there is a number that satisfies none of the cards:

Yes, there is. 32 is the smallest number. To find a number like this, we can first consider about the ones digit. The digit can neither be odd, nor it can be 1, 6 or 8. So the number must have its ones digit being 2, 4 or 0. Next, the number cannot be a multiple of 3 or 7, but it must be a multiple of 4. Then, the number is better to be larger than 60, to avoid it being a factor of 24 or 60. What is remaining to test is whether it is a square number, a triangular number, or one less then a square number. These numbers are not considered. Then the remaining numbers are what we want to find. Using this method, we can find that the numbers that have this feature in 100 are 32, 40, 44, 52 and 92.

Well done finding all these numbers. Ariel! Are there any other possible answers? How do you know?

*You might like to take a look at the problem Satisfying Statements together with the accompanying Teachers' Resources, as the game and the problem have been designed to complement one another.*

You may wish to start your students off with the simplest scoring system, so that they can get used to the game, and then move on to the more challenging versions which might pique students' curiosity and generate interesting insights and discussions:

"If I know that 49 is a square number and a multiple of 7, then I know that 4900 is as well. Or 490000. Or 49000000..."

"If I know that 18, 38, 58, 78 and 98 are even but not multiples of 4, and 2 less than a multiple of 10, then so are 118, 138, 158, 178 and 198. Or 218, 238, 258, 278 and 298, or ..."