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Brainwave 1
Amazing Numbers
There is some amazing information about numbers.
Write down a three digit number, in which all the digits are different, such as 635.
Write down all the possible two digit numbers you can make from the three digit number and then add them together:
63+65+35+56+53+36=308
Note: You should always have six possibilities.
Then add the digits in the original number:
6+3+5=14
Then divide the sum of the two digit numbers (308) by the sum of the digits in the original number (14):
308/14=22
Repeat the process with two other three digit number, in which all the digits are different. What did you find?
What happens if you only use odd numbers or even numbers in the three digit number?
What happens if the digits are repeated eg 363?
Feature Solution
The feature solution for the problem came from 3/4F from Chatham PS.
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What did you have to find out?
We had to find out if there was a pattern if we followed the above provedure. And if the pattern stayed if we used odd or even numbers or repeated digits like 363?
What materials did you use?
Blackboard, paper, pencils, calculators and our brains.
How did you think? What strategies did you use? How did you solve this problem?
We broke up into small groups and each group was given a type of 3 digit number,
1. 3 digit number where all the digits were different
2. 3 digit number where all the digits were even numbers
3. 3 digit number where all the digits were odd numbers
With each 3 digit number we went through the process of finding the 2 digit numbers and adding them together and then dividing the total by the sum of the 3 digits.
After we had established there was a pattern and the answer always stayed the same, we worked as a class to see if the answer was different if one of the digits repeated (e.g 232).
What answers did you come up with?
It didn't matter if the digits were even, odd or a mixture as long as the 3 digits were different the answer always came to be 22.
As for where the digits repeated, the class came up with 2 answers.
1. We wrote down all the possible 2 digit numbers that could be created and included the numbers that repeated, than the answer still came out at 22.
2. However, if we only used different 2 digit numbers, we only came up with 3 different numbers and when you divided the sum of these numbers by the sum of the 3 digits, the answer was 11.
We think it came out at 11, which is half of the original answer because we could only make 3 instead of 6 different 2 digit numbers, which is half the numbers that had to be added together.
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Commendable contributors to the problem were:
Jack & Wayne; Georgia; Sam & Jasmin from Stockinbingal PS
Cindy & Jason from Carlton PS
Mikayla & Emily from Barham PS
Chloe; Jack; Daisy from Tottenham CS |
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Solutions were also sent in by:
Elliot; Jack; Ryan; Nicholas & Oscar from Otford PS
Tim from Greenacre PS
Kyle from Spencer PS |
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