Th e Main Challenge
Pair the ten numbers below so that the difference between the two numbers in each pair is exactly divisible by 7:
6 17 28 37 45 58 64 78 83 98
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 & 3rd rows of the playing board contain the following fourteen numbers:
2 9 13 14 15 22 25 36 40 42 45 66 72 80
What is the sum of the factors of 80 listed above?
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 NINE different ways to make 205 when using Lagrange’s Theorem. How many can you find?
The Mathematically Possible Challenge
Using 5, 7 and 11 once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?
10 20 30 40 50 60 70 80 90 100
#10TimesTable
The Target Challenge
Can you arrive at 205 by inserting 2, 10, 11 and 15 into the gaps on each line?
- (◯×◯×◯)–◯ = 205
- (◯+◯÷◯)×◯ = 205
Answers can be found here.
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