T he Main Challenge
Following on from DAY 187, here’s another one of the unique Keith Number challenges. This was made famous by Mike Keith and if you like playing around with numbers, you’ll love having a go at this fun concept.
The 1st 2-digit Keith Number, 14, is worked out by following a pattern:
- 1+4=5; 4+5=9; 5+9=14 (the total arrives back to the original number).
The 2nd 2-digit Keith Number, 19, is worked out in a similar way:
- 1+9=10; 9+10=19 (again, the total arrives back to the original number).
By following this Fibonacci-style pattern, find the 3rd and 4th 2-digit Keith Numbers.
(Hint: both are less than 50)
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 3rd & 6th rows of the playing board contain the following fourteen numbers:
5 12 13 18 20 25 33 36 42 45 49 56 66 80
Can you find three different numbers listed that add up to exactly 100?
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 different ways to make 240 when using Lagrange’s Theorem. Can you find them?
The Mathematically Possible Challenge
Using 2, 5 and 10 once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?
7 14 21 28 35 42 49 56 63 70
The Target Challenge
Can you arrive at 240 by inserting 1, 2, 3, 4 and 5 into the gaps below?
- ◯²×◯×◯×(◯–◯) = 240
Answers can be found here.
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