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Jere had a bright opening two rounds but his winning streak was halted by Egyptian Grand Master (GM) Ahmed Adly in round three before recovering to force a draw off Belgian GM Vadim Malakhatov. Jere lost to Adly on board two.
Before Jere drew his game with Malakhatov in round four, the Belgian GM had lost his previous game to French GM Vladislav Tkachiev on board one.
The Zambian is now on 2.5 points after four rounds, a point behind French GM Vladislav Tkachiev and Adly.
GM Abergel Thal of France was on three points and in third position.
Jere remains to compete on the top tables and the Zambian IM was on board two on black pieces against GM Tkachiev in round five while GM Thal had white pieces playing GM Adly on board one.
Zimbabwe’s IM Robert Gwaze had two points after four rounds and was paired to play Joao Simoes of Angola.
But it was joy for Zambia Woman FIDE Master (WFM) Lorita Mwango who won both her matches on Monday to move to fourth place in the Cuca Women International championship.
Mwango has three points, half a point behind joint leaders Woman Grand Masters (WGM) Anna Zozulia of Belgium and Katarzyna Toma of Poland.
Paired against easy opponents, the seed eight Mwango took full advantage of her position to reap off 16th seed Luzia Pina of Angola and a seed 15 Portuguese WFM Marita Valdes in rounds three and four respectively.
But it was tough going for WFM Epah Tembo who drew in round three but lost her next game.
In round three, she drew with Women International Master (WIM) Boikhutso of Botswana but lost to lowly ranked Irineia Gabriel of Angola.
In round five, Tembo was to play the Portuguese Valdes with Mwango facing the top seed Zozulia.