Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
Weekly Problem 49 - 2013
What is the value of 2000 + 1999 × 2000?
The numbers 72, 8, 24, 10, 5, 45, 36, 15 are grouped in pairs so that each pair has the same product. Which number is paired with 10?
We received lots of great solutions to this question. One student noticed:
If it is Monday today, then in 7 days it will be Monday again, then in 14 days, than 21 and so on. This goes on like the 7 times table: any number divisible by 7 will be a Monday.
If today is Monday, in 29 days what day will it be?
Well, 29/7 = 4 with remainder 1, so in 29 days it will be 1 day after Monday,
i.e. Tuesday. So it matters what the remainder is.
Charlie and Alison's statements were all correct, and we received great explanations of this from Jebin and Matthew from Junior King's School Canterbury, Alastair from St Mary's Primary School in Yorkshire, Cherice from Taipei European School and Sam from Shrewsbury House School. Alastair wrote:
Charlie is right with his numbers because they are all multiples of 7; therefore all will be Mondays. Alison is right because her numbers are all multiples of 7 plus two; therefore all will be Wednesdays.
Lots of students correctly pointed out that, if today is Monday, then in 1000 days it will be Sunday. For example, Nicholas from Brazil used Ann's method and added on multiples of 7 to get closer to 1000:
It will be Monday in 700 days, 770 days, 840 days, 910 days, 980 days, 987 days and 994 days, and then 6 days later it is Sunday.
Many students also commented on Luke's method. Here is one very clear explanation we received from Yasmine at Garden School, Kuala Lumpur:
First I divided 1000 by 7, which gave 142.8571429. I rounded this down to 142, then multiplied 142 by 7, to give me 994. This means that 994 days is exactly 142 weeks - so in 994 days, it's still Monday. Since we want to know what happens in 1000 days, we just add 6 days to Monday, and find that the answer is Sunday.
George from England pointed out that this is the same as saying that 1000/7 = 142 remainder 6.
We received responses to the later questions from Tom from Monmouth School, Noor-ul-Ain from Westfield Middle School, Sam from Shrewsbury House School, Alastair from St Mary's Primary, and Katherine, Jack, Fred, Megan, Amani, Jasmine, Fiona, Michael, Jet, Markus and Gaeti from Garden School, Kuala Lumpur. Here are some of them: