# Solve it Sunday: Fibonacci’s Game

This mathematical party game was devised in the thirteenth century by the Italian mathematician Leonardo Pisano, known to the modern world as Fibonacci. His work on the mathematical system helped to set up the Renaissance, but the matter we will address here is less weighty.

Between two and nine people sit in a line, and together, they secretly conspire to select one of their number.

This person picks a finger joint of one of their hands, either where their ring is being worn, or where the volunteer nominates as a spot where he or she would like to have a ring.

The volunteer then takes their position in the line, doubles it, adds 5, multiplies by 5, and then adds 10 to the total.

Then the number of the ring-bearing finger across the two hands is counted and added (starting with the left little finger as 1), and the value is multiplied by 10.

Finally a number for the knuckle joint is added on, 1 for the joint nearest the hand, 3 for the tip joint. This gives a final total.

“When the number is announced,” Fibonacci says, “it is easy to pinpoint the ring.”

Can you see how?

## One Reply to “Solve it Sunday: Fibonacci’s Game”

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Through the various multiplications, the different elements of the ANSWER – position in line, finger number and joint number – are put into separate digits of the final total. Take away 350, the base value of the set of calculations and the digits of the result give you seat, finger and joint in that order.

For example, someone in the 8th seat, with a ring on the 2nd joint of finger 4, will result in a total of 8×2=16, +5 =21, x5 =105, +10 =115. (115+4) x 10 = 1190, and +2 = 1192.

Then, for the performer, 1192-350 = 842, which breaks back down to 8-4-2.

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