The Main Challenge
All nine numbers from 21 to 29 inclusive must be allocated to a letter below so that each allocated number satisfies the condition given on the line:
- (a) even number,
- (b) factor of 144,
- (c) power of 3,
- (d) prime number,
- (e) digits which differ by 1,
- (f) exactly 3 factors,
- (g) multiple of 7,
- (h) equal to the sum of all its factors (except the number itself),
- (i) 2nd digit is greater than its 1st digit.
Remember, the numbers 21 to 29 should only appear once each.
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 & 7th rows contain the following fourteen numbers:
2 4 9 11 14 15 22 24 27 30 40 70 72 77
Which odd number, when 21 is added to it, becomes a square number?
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 THREE ways of making 18 when using Lagrange’s Theorem. Can you find them?
The Mathematically Possible Challenge
Using 5, 6 and 8 once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?
9 18 27 36 45 54 63 72 81 90
#9TimesTable
The Target Challenge
Can you arrive at 18 by inserting 2, 3, 4 and 6 into the gaps on each line?
- ◯×◯–◯×◯ = 18
- ◯÷◯×◯×◯² = 18
- (◯÷◯)³×√◯÷◯ = 18
Answers can be found here.
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