Normal sudoku rules apply. A clue outside the grid indicates the presence of a thermometer that is fully placed in the direction of the arrow where all the digits on the thermometer add to the number of the clue and the bulb is always the closest to the clue. Digits on a thermometer are all different and strictly increasing from the bulb to the tip. Thermometers are mimimally three cells long and they include all possible digits. i.e. the first digit behind the thermometer may not be larger than the last digit on the thermometer, and the last digit before a thermometer may not be smaller than the digit in the bulb. Thermometers may overlap other thermometers.