DAY 210:

The Main Challenge

Try the following Mathelona challenge, similar to my pocket book challenges but slightly tougher!  Full details at Mathelona.

Your task is to make all four lines work out arithmetically by placing the 16 digits listed below into the 16 gaps.  Can you  achieve it?

0    0    1    1    2    2    3    3    4    4    5    6    6    7    8    9

◯  +  ◯   =    8    =   ◯  +  ◯
◯  +  ◯   =    7    =   ◯  –  ◯
◯  +  ◯   =    6    =   ◯  ×  ◯
◯  +  ◯   =    4    =   ◯  ÷  ◯

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 2nd & 5th rows of the playing board contain the following fourteen numbers:

6   7   8   16   17   21   28   48   50   55   63   64   81   84

How many factors does the smallest number in the list have?

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 THIRTEEN different ways to make 210 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 57 and 11 once each, with + – × ÷ available, which are the only THREE 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 210 by inserting 5, 10, 12 and 18 into the gaps on each line?

  •  ◯×◯+◯×◯ = 210
  •  (◯–◯÷◯)×◯ = 210

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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