T he Main Challenge
When multiplying two numbers together and then adding or subtracting a third number, there are four ways of reaching 60 when the three numbers used in each calculation are in the range 1-9 (which can be repeated).
One way to make 60 is (9×6)+6; can you find the other three?
[Note: (9×6)+6 and (6×9)+6 counts as just one way.]
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 & 5th rows contain the following fourteen numbers:
6 7 13 16 21 25 36 42 45 50 66 80 81 84
How many pairs of consecutive numbers are there?
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 66 when using Lagrange’s Theorem. Can you find them all?
The Mathematically Possible Challenge
Using 4, 6 and 12 once each, with + – × ÷ available, which SIX numbers is it possible to make from the list below?
3 6 9 12 15 18 21 24 27 30
#3TimesTable
The Target Challenge
Can you arrive at 66 by inserting 2, 3, 4 and 9 into the gaps on each line?
- (◯×◯+◯)×◯ = 66
- (◯×◯–◯)×◯ = 66
- ◯²×◯+◯×◯ = 66
- ◯³+(◯+◯)²+√◯ = 66
Answers can be found here.
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