Amal wants to place all the numbers 1 to 10 in the circles in the diagram with one number in each circle. She wants the sum of the numbers in any four circles that are in a straight line to be 23 , for example the sum of numbers in four grey circles is 23 . What number must she place in the circle containing the question mark?

Solution

A ma l w an t s t o pl a ce a ll t h e n u mb ers 1 t o 10 in t h e c i rc l es in t h e d ia g r am w i t h o n e n u mb er in e a c h c i rc l e . S h e w an t s t h e s u m o f t h e n u mb ers in an y f o u r c i rc l es t ha t a re in a s t r ai g h t l in e t o b e 23, f or e x am pl e t h e s u m o f n u mb ers in f o u r g rey c i rc l es i s 23 . Wha t n u mb er m u s t s h e pl a ce in t h e c i rc l e co n t ainin g t h e q u es t i o n ma r k ?

The number : 23 or - 23

Solution steps

Represent the number with

x

A.T.Q.:

x (x) = 23

Solve for

x, x (x) = 23 : x = 23, x = - 23

The number : 23 or - 23