T he Main Challenge
A palindromic number is a number that can be read the same forwards and backwards (e.g. 333 and 797). How many palindromic numbers are there between 100 and 1,000?
The 7puzzle Challenge
The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 2 up to 84.
The 1st & 7th rows contain the following fourteen numbers:
2 4 9 11 14 15 22 24 27 30 40 70 72 77
What is the sum of the multiples of 9?
The Lagrange Challenge
Lagrange’s Four-Square Theorem states that every positive 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).
There are SIX ways of making 124 when using Lagrange’s Theorem. Can you find them?
The Mathematically Possible Challenge
Using 2, 4 and 12 once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?
1 4 9 16 25 36 49 64 81 100
#SquareNumbers
The Target Challenge
Can you arrive at 124 by inserting 5, 8, 10 and 16 into the gaps on each line?
- (◯+◯)×◯+√◯ = 124
- ◯×◯–(◯÷◯)² = 124
- (◯–◯÷◯)×◯ = 124
Answers can be found here.
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