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We present the results of an ongoing project to use the X-ray observations of Type Ia Supernova Remnants to constrain the physical processes involved in Type Ia Supernova explosions. We use the Tycho Supernova Remnant (SN 1572) as a benchmark case, comparing its observed spectrum with models for the X-ray emission from the shocked ejecta generated from different kinds of Type Ia explosions. Both the integrated spectrum of Tycho and the spatial distribution of the Fe and Si emission in the remnant are well reproduced by delayed detonation models with stratified ejecta. All the other Type Ia explosion models fail, including well-mixed deflagrations calculated in three dimensions.