# Sum-Up

Also Known As:

Summing Up, Weighed Up

A simple mathematical, logical puzzle. Given the total values for several combinations of typically four objects, you are required to calculate the value of each individual object. It is not necessary to guess, or use trial and error. The best approach is to express this puzzle in terms of simple algebra.

For example, consider this problem:

one pebble and three sea urchins cost £30.

two pebbles and two starfish cost £18.

a pebble, a sea urchin, a starfish and a sea-shell cost £26.

two pebbles, a sea urchin and a sea-shell cost £23.

If we think of the pebble as a, the sea urchin as b, the starfish as c and the seashell as d, then:

a+3b=£30

2a+2c=£18

a+b+c+d=£26

2a+b+d=£23

If 2a+2c=£18, then a+c=£9. This means that £9+b+d=£26, so b+d=£17. From here (see 2a+b+d=£23) the answer is easy to calculate.

Another common version of this puzzle is called Weighed Up. Here, the solver is given several pictures showing how various combinations of objects balance one another, and is required to calculate how many of a particular object will be required to make a final set of objects balance.

Instructions

Using the totals given, calculate the price of each of the pictured items.

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