Another great problem from Matt Enlow’s collection

Today we talked about another problem from the amazing list of problems that Matt Enlow’s published a few weeks ago:

This is our second project from that collection. The first is here:

Sharing a neat problem from Matt Enlow with kids

For today’s problem I introduced the problem and asked the boys for their initial thoughts. My older son noticed an important property about the sum of 9 and consecutive integers. He explained the property that the sum of 11 consecutive numbers would have and then my younger son explained the similar property that the sum of 9 consecutive numbers would have:

Next we had to see if there were any special properties that the sum of 10 consecutive integers would have.

Once we had that property, my younger son was able to explain how you could use them to find a number that would work (though not necessarily the smallest one):

At the end of the last video we though that 495 would satisfy the conditions of the problem. Here we checked that it did and wondered if it was the smallest.

Finally, we checked to see if 495 was indeed the smallest positive number with the properties in the problem.

My older son thought that 0 would have worked, but working it out he saw that it didn’t.

After that, we saw that 495 was indeed the smallest.

Definitely a great problem – it is nice to hear the boys explain some basic ideas in number theory. It is also a nice problem because kids – well, at least my kids – often struggle to see the difference between “find the smallest” and “find an example” and this problem helps show that “find the smallest” requires a bit more work.