T he Main Challenge
You roll two normal six-sided dice, both containing the numbers 1-6. When multiplying the two numbers that show, how many DIFFERENT answers is it possible to obtain?
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 3rd & 7th rows contain the following fourteen numbers:
4 11 13 24 25 27 30 36 42 45 66 70 77 80
What is the sum of the factors of 90?
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 FOUR ways of making 49 when using Lagrange’s Theorem. Can you find them?
The Mathematically Possible Challenge
Using 8, 9 and 10 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?
10 20 30 40 50 60 70 80 90 100
#10TimesTables
The Target Challenge
Can you arrive at 49 by inserting 1, 2, 3 and 4 into the gaps on each line?
- (◯+◯)²×(◯–◯)² = 49
- (◯+◯)²×√◯–◯ = 49
- ◯⁶–(◯+◯)×◯ = 49
Answers can be found here.
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