day/dydd 237 at 7puzzleblog.com

T he Main Challenge

A young mathematician originally from Nigeria called Chika, who now lives in London, has come up with a brilliant way of testing whether a number is divisible by 7.

Multiply the unit digit by 5. Keep the answer to one side! Treat the rest of the digits as a separate number and add it to your stored number. If this sum is divisible by 7, your original number is a multiple of 7, easy!!

If the sum is itself a big number, you can repeat the process with this new number.

For example, we shall test this theory by using 406:

  • Multiply the unit number (6) by 5, which gives us 30,
  • The rest of the number (40) is added to 30 (from above), giving us 70,
  • Is 70 a multiple of 7? YES, therefore 406 is a multiple of 7.

Using the above algorithm, which TWO of the following are NOT multiples of 7?

245    308    476    557    693    735    811    994

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 3rd & 6th rows of the playing board contain the following fourteen numbers:

5   12   13   18   20   25   33   36   42   45   49   56   66   80

What is the difference between the totals of the odd numbers and even numbers?

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 ELEVEN different ways to make 237 when using Lagrange’s Theorem. How many of them can you find?

The Mathematically Possible Challenge

Using 25 and 10 once each, with + – × ÷ available, which are the only THREE numbers it is 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 237 by inserting 1, 2, 3, 4 and 5 into the gaps below?

  •  (◯+◯)²×(◯+◯)–double◯ = 237

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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