T he Main Challenge
Read the facts below:
- I am a 2-digit number,
- I am a multiple of 7,
- The difference between my two digits is 4.
Which number am I?
The 7puzzle Challenge
The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from 2 up to 84.
The 3rd & 5th rows contain the following fourteen numbers:
6 7 13 16 21 25 36 42 45 50 66 80 81 84
Which number, when 1 is subtracted from it, becomes a square number?
The Lagrange Challenge
Lagrange’s Four-Square Theorem states that every integer can be made by adding up to four square numbers.
For example, 7 can be made by 2²+1²+1²+1² (or 4+1+1+1).
Show how you can make 174, in NINE different ways, when using Lagrange’s Theorem.
The Mathematically Possible Challenge
Using 4, 6 and 10 once each, with + – × ÷ available, which THREE target numbers is it possible to make from the list below?
1 3 6 10 15 21 28 36 45 55 66
#TriangularNumbers
The Target Challenge
Can you arrive at 174 by inserting 9, 10, 16 and 20 into the gaps on each line?
- (◯+◯)×(◯–◯) = 174
- ◯×◯+◯–◯ = 174
Answers can be found here.
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