T he Main Challenge
There are two sets of three consecutive numbers, in ascending order, whose sum is less than 50 and follow this sequence:
- triangular number – square number – prime number
Can you list both sets of numbers?
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 3rd & 6th rows of the playing board contain the following fourteen numbers:
5 12 13 18 20 25 33 36 42 45 49 56 66 80
What is the difference between the totals of the odd numbers and even numbers?
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 ELEVEN different ways to make 237 when using Lagrange’s Theorem. How many of them can you find?
The Mathematically Possible Challenge
Using 2, 5 and 10 once each, with + – × ÷ available, which are the only THREE numbers it is 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 237 by inserting 1, 2, 3, 4 and 5 into the gaps below?
- (◯+◯)²×(◯+◯)–double◯ = 237
Answers can be found here.
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