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Number Round Up

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

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Grouping Goodies

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

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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.

More Numbers in the Ring

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Vidhya from Kensri School in India sent in a very well reasoned solution:

When we subtract an even number from an odd number, or vice versa, the difference is always odd. So if we fill up odd numbers and even numbers alternately, if there are an even number of squares, the differences will all be odd. But there is no solution (in other words the differences cannot all be odd) if there is an odd number of squares.