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Puzzle - Answer

BricksImagine that you are building a tower of play bricks.

A yellow brick is 19 millimetres tall and a green brick is 21 millimetres tall.

How many of each are required to build a tower that is exactly 562 millimetres tall?

 [Ref: ZFQY] © Kevin Stone

Answer: 13 yellow and 15 green bricks.

We are after Y lots of 19 plus G lots of 21 to equal 562.

   19Y + 21G = 562

It is easiest to try different values for Y, until one gives an answer divisible by 21:

   21G = 562 - 19Y

Y = 1 >> 21G = 562 - 19 = 543   x
Y = 2 >> 21G = 562 - 38 = 524   x
Y = 3 >> 21G = 562 - 57 = 505   x
Y = 4 >> 21G = 562 - 76 = 486   x
Y = 5 >> 21G = 562 - 95 = 467   x
Y = 6 >> 21G = 562 - 114 = 448   x
Y = 7 >> 21G = 562 - 133 = 429   x
Y = 8 >> 21G = 562 - 152 = 410   x
Y = 9 >> 21G = 562 - 171 = 391   x
Y = 10 >> 21G = 562 - 190 = 372   x
Y = 11 >> 21G = 562 - 209 = 353   x
Y = 12 >> 21G = 562 - 228 = 334   x
Y = 13 >> 21G = 562 - 247 = 315   OK

Y = 13, therefore G = 315 ÷ 21 = 15. QED.

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