T he Main Challenge
Firstly, write down three separate lists only containing numbers in the range 1 to 100:
- List 1 – multiples of 9
- List 2 – factors of 108
- List 3 – triangular numbers
Part 1: Which is the only number present on all three lists?
Part 2: List the eight other numbers that are on exactly two of the lists?
Part 3: How many DIFFERENT numbers are written on the three lists?
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 2nd & 4th rows of the playing board contain the following fourteen numbers:
3 8 10 17 28 32 35 44 48 54 55 60 63 64
From the list, what is the sum of the 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 EIGHT different ways to make 233 when using Lagrange’s Theorem. How many of them can you find?
The Mathematically Possible Challenge
Using 2, 4 and 8 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?
2 3 5 7 11 13 17 19 23 29
#PrimeNumbers
The Target Challenge
Can you arrive at 233 by inserting 11, 12, 13, 14 and 15 into the gaps below?
- 6×◯+5×◯+4×◯+3×◯–◯ = 233
Answers can be found here.
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