Cassandra (12 years) from Impington Village College (Cambridge) says that the 5 appears 170 times on a 24 hour clock and has clearly explained how she worked that out.

``I counted how many times the 5 was in the units of the minutes (01:25) in the hour (6 times) then multiplied it by 24 (144).

Then I counted how many times the 5 appeared in the tens of minutes (12:50) in 24 hours (24).

Finally I counted how many times it appears in the hours section (05:00) (2).

I added it all up and got 170. The answer is the same for the 12 hour clock, because there's just two 5 o'clocks instead of 05:00 and 15:00.''

Solution 2

Another solution came in from Jonathan (10 years) from St. Andrews Primary (Devon). This is quite a different solution to Cassandra's because Jonathon looked at the problem in a different way. When Jonathan worked out his total, he counted the 5's that would be on the clock if he looked at it every minute. So, for example, at 05:53 there's two, then at 05:54 there's two, and at 05:55 there's three and so on. Here is his explanation:

``My answer is 504. This is how I worked it out. I worked out that 5 appears 16 times in 22 hours (05, 15, 25, 35, 45, 50, 52, 53, 54, 55, 56, 57, 58, 59), but I had to add 60 more 5s when the hour was 5 or 15 to make 76.

I multiplied 16 x 22 to make 352, added 2 x 76 (152) to make my total.

Here is the sum to show what I did: (16 X 22) + (76 X 2) = 504.

Yes I think it is the same with a twelve hour clock, it just has 2 5s instead of 15.''