# Solution to Enigma No. 1526

31 December 2008

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Answer: The true temperature was 80ºC

The winner is Mike Waterman of Camberley, Surrey, UK. There were 124 entries.

## Notation

• TC = Temperature indicated in ºC
• TF = Temperature indicated in ºF
• TT = True temperature in ºC
• EC = Error Factor – ºC Measurement
• EF = Error Factor – ºF Measurement

## Basic Formulae

• TC = TT . EC…..(1)
• TF = (TT . 9/5 + 32). EF…..(2)
• TT = TC/EC = (TF/EF – 32). 5/9…..(3)

## Calculations

• TC = 76.3
• TF = 150.1
• 76.3/EC = (150.1/EF – 32) . 5/9…..(3)
• TC = 98.1
• TF = 184.3
• 98.1/EC = (184.3/EF – 32) . 5/9…..(3)

## Eliminating EC

• 76.3 (184.3/EF – 32) = 98.1 (150.1/EF – 32)
• EF = 0.95
• With TF = 167.2
• &
• TT = (TF/EF – 32) . 5/9…..(2)
• TT= (167.2/0.95-32) . 5/9=80

Solution = 80ºC

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