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?
Age
11 to 14
Challenge level
Problem
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.
Student Solutions
Answer:
2 - odd
5 - divisible by 7
7 - greater than 100
12 - prime
Below, the numbers are connected to the properties they satisfy
Image
7 and "prime" both have three lines, leaving only one possibility for their backs:
Image
5 is odd so 2 must be on the back of "odd":
Image
