# DAY/DYDD/GIORNO/NAP 187: T he Main Challenge

A Keith Number, made famous by Mike Keith, is worked out in a not-too-dissimilar way to Fibonacci Numbers. If you like playing around with numbers, have a go at this fun concept.  The first 2-digit Keith Number, 14, is worked out as follows:

• Try 14: 1+4=5; 4+5=9; 5+9=14 (the total arrives back to the original number).

By following this pattern, can you find the next 2-digit Keith Number?

[Hint: it’s not too far away!] The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from up to 84.

The 2nd & 3rd rows contain the following fourteen numbers:

8   13   17   25   28   36   42   45   48   55   63   64   66   80

Which three numbers, when 6 is added to them, each become multiples of 7? The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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).

Show how you can make 187, in NINE different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 34 and 12 once each, with + – × ÷ available, which THREE numbers are not possible to make from the list below?

4    8    12    16    20    24    28    32    36    40

#4TimesTable The Target Challenge

Can you arrive at 187 by inserting 457 and 9 into the gaps on each line?

•  (◯×◯×◯)+◯ = 187
•  ◯²×◯+◯×√◯ = 187   