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6 Beads

If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

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Writing Digits

Lee was writing all the counting numbers from 1 to 20. She stopped for a rest after writing seventeen digits. What was the last number she wrote?

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What Number?

I am less than 25. My ones digit is twice my tens digit. My digits add up to an even number.

Two-digit Targets

Stage: 1 Challenge Level: Challenge Level:1
We had some good solutions sent in, first from Matt, George, Charlotte, Shimelia, Jonty, Isaac and Zak at Waterbeach Primary School we had the following:

First everyone tried to come up with a solution. Here are some of our ideas;

Solution 1:
Largest even number: 98
Largest odd number: 73
Smallest odd number: 01
Largest multiple of 5: 65
Number closest to 50: 42

Solution 2;
Largest even number: 90
Largest odd number: 87
Smallest odd number: 13
Largest multiple of 5: 25
Number closest to 50: 26

Solution 3:
Largest even number: 98
Largest odd number: 63
Smallest odd number: 27
Largest multiple of 5: 15
Number closest to 50: 40

Then we tried to work out which solution was better. We looked at solution 1 and solution 2. We found out it was easy to say which solution was better if you just look at one thing (e.g. largest even number), but it’s much more difficult if you want to find the best overall solution for all the things!

We thought about what was the best solution if we didn’t keep to the rules! It would be;
Largest even number: 98
Largest odd number: 99
Smallest odd number: 01
Largest multiple of 5: 95
Number closest to 50: 50

Then we thought about if we could test the best solution. One person suggested we look at the difference between the ‘best’ solution and the solutions we came up with.

  Solution 1 Solution 2
Largest even number 98 – 98 = 0 98 – 90 = 8
Largest odd number 99 – 73 = 26 99 – 87 = 12
Smallest odd number 01 – 01 = 0 13 – 01 = 12
Largest multiple of 5 95 – 65 = 30 95 – 25= 70
Number Closest to 50 50 – 42 = 8 50 – 46 =4

 
Solution 1 was better three times, solution 2 was better two times.
We suggested adding up the differences to test which was better.
Solution 1 differences add up to 64
Solution 2 differences add up to 106
So Solution 1 was better!

We tried to come up with a better solution!
We decided the biggest digits needed to go in the 10s column when you need a large answer. We decided to put the 0 in the 10s column for the smallest odd number. This was our new solution;
Largest even number: 96
Largest odd number: 83
Smallest odd number: 01
Largest multiple of 5: 75
Number closest to 50: 42
This had a total difference of 46, so it was better!

We felt this was a good presentation of their working and results, thank you and well done!  Karel at Our Lady of Good Council Boys School in Ireland we sent the following;


largest even number: 98
largest odd number: 75
smallest odd number: 13
largest multiple of 5: 60
number closest to 50: 42

"Can you find other ways of doing it?"

No, but the order is important you could even get stuck if you start from the bottom, the answer is 50, and without 5 and 0, you can not make multiples of 5 anymore for the next question.

It may be worthwhile exploring how it is that there are different solutions. I wonder how many acceptable solutions there are?