# DAY/DYDD/PÄIVÄ/NAP 153 at 7puzzleblog.com Th e Main Challenge

Using the three numbers 4, 4 and 4 once each, with + – × ÷ available, there are just SIX target numbers from 1-30 that are mathematically possible to achieve.  Can you find them? 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

Which number, when 15 is subtracted from it, becomes a multiple 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 (4+1+1+1).

Show how you can make 153, 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?

4    8    12    16    20    24    28    32    36    40

#4TimesTable The Target Challenge

Can you arrive at 153 by inserting 346 and 7 into the gaps in each line below?

•  (◯×◯–◯)×◯² = 153
•  ◯+◯×treble(◯+◯) = 153   