What's on the Back?
Four cards have a number on one side and a phrase on the back. On each card, the number does not have the property described on the back. What do the four cards have on them?
Four cards each have a number written on one side and a phrase written on the other. The four numbers are $2$, $5$, $7$ and $12$.
The four phrases are
Divisible by $7$
Odd
Prime
Greater than $100$
Odd
Prime
Greater than $100$
On each card, the number written does not have the property written on the other side of the card. What are the four number-property pairs?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Answer:
2 - odd
5 - divisible by 7
7 - greater than 100
12 - prime
Below, the numbers are connected to the properties they satisfy
Image
![What's on the Back? What's on the Back?](/sites/default/files/styles/large/public/thumbnails/content-id-11708-whats%252520on%252520the%252520back%252520properties.png?itok=ZByqf5ac)
7 and "prime" both have three lines, leaving only one possibility for their backs:
Image
![What's on the Back? What's on the Back?](/sites/default/files/styles/large/public/thumbnails/content-id-11708-whats%252520on%252520the%252520back%2525207%252520and%25252012.png?itok=YXITqAvi)
5 is odd so 2 must be on the back of "odd":
Image
![What's on the Back? What's on the Back?](/sites/default/files/styles/large/public/thumbnails/content-id-11708-whats%252520on%252520the%252520back%2525205%252520and%2525202.png?itok=r6G6bu3h)