T he Main Challenge
Each of the five numbers below is the product of two prime numbers:
15 35 77 143 323
… but which is the odd one out when looking at each calculation that arrived at these answers?
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 5th & 6th rows of the playing board contain the following fourteen numbers:
5 6 7 12 16 18 20 21 33 49 50 56 81 84
What is the sum of the multiples of 7?
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 FOURTEEN different ways to make 225 when using Lagrange’s Theorem. How many can you find?
The Mathematically Possible Challenge
Using 4, 6 and 9 once each, with + – × ÷ available, which are the FOUR numbers it is possible to make from the list below?
15 30 45 60 75 90 105 120 135 150
#15TimesTable
The Target Challenge
Can you arrive at 225 by inserting 3, 4, 5 and 9 into the gaps on each line?
- (◯–◯)×◯×◯² = 225 (there are 2 ways!)
- (◯+◯+◯–◯)² = 225
Answers can be found here.
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