# day/dydd 200 at 7puzzleblog.com

The Main  Challenge

Playing the superb American maths card game, 24game®, can be frustrating but very addictive when testing your arithmetical skills.

When using four numbers just once each, with + – × ÷ available, it is only possible to make 24 with only ONE of the seven groups of numbers below:

•      1    1    7    6
•      1    1    7    7
•      1    1    7    8
•      1    1    7    9
•      1    1    7   10
•      1    1    7   11
•      1    1    7   12

. . . but which one?

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 is the only cube number listed?

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 FIVE different ways to make 200 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Using 57 and 11 once each, with + – × ÷ available, which is the ONLY number it is 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 200 by inserting 101525 and 30 into the gaps on each line?

•  ◯×◯–◯×◯ = 200
•  (◯–◯÷◯)×◯ = 200