T he Main Challenge
A Keith Number, made famous by Mike Keith, is worked out in a not-too-dissimilar way to Fibonacci Numbers. If you like playing around with numbers, have a go at this fun concept. The first 2-digit Keith Number, 14, is worked out as follows:
- Try 14: 1+4=5; 4+5=9; 5+9=14 (the total arrives back to the original number).
By following this pattern, can you find the next 2-digit Keith Number?
[Hint: it’s not too far away!]
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 2nd & 3rd rows contain the following fourteen numbers:
8 13 17 25 28 36 42 45 48 55 63 64 66 80
Which three numbers, when 6 is added to them, each become multiples of 7?
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 187, in NINE different ways, when using Lagrange’s Theorem.
The Mathematically Possible Challenge
Using 3, 4 and 12 once each, with + – × ÷ available, which THREE numbers are not possible to make from the list below?
4 8 12 16 20 24 28 32 36 40
#4TimesTable
The Target Challenge
Can you arrive at 187 by inserting 4, 5, 7 and 9 into the gaps on each line?
- (◯×◯×◯)+◯ = 187
- ◯²×◯+◯×√◯ = 187
Answers can be found here.
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