# DAY/DYDD 199: T he Main Challenge

From the numbers in the range 1-50, eliminate the following:

•  multiples of 3
•  square numbers
•  prime numbers
•  even numbers

Which number is the only one that remains? 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 6th & 7th rows of the playing board contain the following fourteen numbers:

4   5   11   12   18   20   24   27   30   33   49   56   70   77

Which number, when 20 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 SEVEN different ways to make 199 when using Lagrange’s Theorem. How many can you find? The Mathematically Possible Challenge

Using 57 and 11 once each, with + – × ÷ available, which are the only TWO numbers it is 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 199 by inserting 111214 and 20 into the gaps on each line?

•  ◯×◯+◯+◯ = 199
•  ◯²+◯+◯–◯ = 199   