Challenge Level

Here are a few of the solutions we received:

Do human beings live for as long as a million hours?Amy from Frances Bardsley School for Girls concluded that most of us don't:

24 hrs = 1 day365 days = 1 year

24 x 365 = 8760 hrs in a year

8760 x 79 (that's the rough age humans live for) = 692,040 hours, so we do not live for 1million hours.

And students from Jumeirah Primary School came to the same conclusion:

No, because the average human lives for 80 years. This equals 700800 hours, which is less that 1000000.

Saad from JPS in Dubai worked out that just a few of us do:

24 hours = 1day.24 hours x 365 = 8760 hours per year.

10 years = 87600 hours

50 years = 43800 hours

100 years = 876000 hours

105 years = 919800 hours

110 years = 963600 hours

112 years = 981120 hours

114 years = 998640 hours

114.10 years = 999516 hours

114.13years = 999788.8 hours

114.1551 years = 999998.676 hours

114.1552 years = 999999.52 hours

114.1553 years = 1000000.428 hours

If you have been alive for a million seconds, how many birthdays have you had?

Linden from HighdownSchool worked out that there would be no birthdays:

1000000 seconds / 60 =16667 mintues16667 mintues / 60 = 278 hours

278 hours / 24 = 12 days

Birthdays = 0

Alex from Welsey Collegecame to the same conclusion:

You wouldn't have been able to have a birthday 1
million seconds ago because 1 year's worth of seconds are
31,622,400

How long would it take to count to a million?

Alex from Toot Hill's Junior Maths Academy (Mathletes) had a go at this problem:

I broke the numbers down into groups, because I needed to find
the average for the time taken to say the different numbers of
digits.

Time taken to read single digit numbers: 4 seconds for all 9
numbers

Time taken to read double digit numbers: 5 seconds for 10
numbers, so 45 seconds for all 90 numbers

Time taken to read triple digit numbers: 9 seconds for 10
numbers, so 810 seconds for all 900 numbers

Time taken to read four digit numbers: 18 seconds for 10
numbers, so 16200 seconds for all 9000 numbers

Time taken to read five digit numbers: 18 seconds for 10
numbers, so 162000 seconds for all 90000 numbers

Time taken to read six digit numbers: 23 seconds for 10
numbers, so 2070000 seconds for all 900000 numbers

Time taken to read seven digit number: 1 second for one
number

So 2249060 seconds to countall one million numbers.

2249060 seconds is 37484.3 minutes which is 624.7 hours which
is 26 days.

This would work if you make the assumptions:

that you talk at a constant speed;

that you don't eat or drink or sleep...!

Thank you all for your clear explanations.