# DAY/DYDD/GIORNO/NAP 154: Th e Main Challenge

From the following list of eighteen numbers, eliminate all square numbers, multiples of 8, factors of 60 and prime numbers.

3  4  7  10  11  15  16  17  24  27  30  32  36  48  49  54  56  64

What is the sum of the TWO numbers that remain? 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 3rd & 7th rows contain the following fourteen numbers:

4   11   13   24   25   27   30   36   42   45   66   70   77   80

How many even numbers, when halved, become odd numbers? 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 (4+1+1+1).

Show how you can make 154, in TEN different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using the three digits 35 and 8 once each, with + – × ÷ available, which are the only TWO numbers it’s possible to make from the list below?

5    10    15    20    25    30    35    40    45    50

#5TimesTable The Target Challenge

Can you arrive at 154 by inserting 567 and 8 into the gaps in each line below?

•  (◯×◯–◯)×◯ = 154
•  ◯²+◯²+◯²+◯ = 154   