DAY 223:

The Main Challenge

Try the following MATHELONA challenge, just like the ones in my number puzzle pocket book.  Further details can be found by clicking on MATHELONA.

Your task is to make all three lines work out arithmetically by replacing the 12 ◯’s below with  0  0  1  1  2  2  3  3  4  4  6  6.  Can you do it?

◯  +  ◯   =    4    =   ◯  –  ◯
◯  +  ◯   =    6    =   ◯  ×  ◯
◯  +  ◯   =    3    =   ◯  ÷  ◯

The 7puzzle Challenge

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

The 5th & 6th rows of the playing board contain the following fourteen numbers:

5   6   7   12   16   18   20   21   33   49   50   56   81   84

What is the answer when the larger multiple of 10 is divided by the smaller one?

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 NINE different ways to make 223 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 46 and once each, with + – × ÷ available, which are the FIVE numbers it is possible to make from the list below?

1    3    5    7    9    11    13    15    17    19

#OddNumbers

The Target Challenge

Can you arrive at 223 by inserting 378 and 20 into the gaps on each line?

  •  ◯²×◯+◯×◯ = 223
  •  (◯⁵–◯)÷(◯–◯) = 223

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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