DAY/DYDD 144:

The Main Challenge

Another mini-Mathelona challenge where your task is to correctly place the eight digits 1 1 1 2 2 3 4 and 5 into the eight gaps so both lines work out arithmetically:

◯  +  ◯   =    3    =   ◯  –  ◯
◯  +  ◯   =    4    =   ◯  ×  ◯

Click Mathelona for details of our popular pocket book of challenges.

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 1st & 4th rows contain the following fourteen numbers:

2   3   9   10   14   15   22   32   35   40   44   54   60   72

Which five numbers listed can be made by adding two others from the list?

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 FOUR ways of making 144 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using the three digits 2, 6 and 9 once each, with + – × ÷ available, which are the only THREE numbers it’s possible to make from the list below?

7    14    21    28    35    42    49    56    63    70

#7TimesTable

The Target Challenge

Can you arrive at 144 by inserting 4, 6, 9 and 12 into the gaps on each line?

  •  ◯×◯×(◯◯) = 144
  •  ◯×◯×double(◯◯) = 144
  •  ◯×◯×(◯÷◯)² = 144
  •  ◯²×(◯+◯–◯) = 144   (2 different ways!)
  •  ◯×◯+treble(◯×√◯) = 144

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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